37
A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS THOMAS EICHNER RÜDIGER PETHIG CESIFO WORKING PAPER NO. 950 CATEGORY 8: RESOURCES AND ENVIRONMENT MAY 2003 An electronic version of the paper may be downloaded from the SSRN website: www.SSRN.com from the CESifo website: www.CESifo.de

A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

  • Upload
    others

  • View
    5

  • Download
    0

Embed Size (px)

Citation preview

Page 1: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

A MICROFOUNDATION OFPREDATOR-PREY DYNAMICS

THOMAS EICHNERRÜDIGER PETHIG

CESIFO WORKING PAPER NO. 950CATEGORY 8: RESOURCES AND ENVIRONMENT

MAY 2003

An electronic version of the paper may be downloaded• from the SSRN website: www.SSRN.com• from the CESifo website: www.CESifo.de

Page 2: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

CESifo Working Paper No. 950

A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS

Abstract

Predator-prey relationships account for an important part of all interactions between species.In this paper we provide a microfoundation for such predator-prey relations in a food chain.Basic entities of our analysis are representative organisms of species modelled similar toeconomic households. With prices as indicators of scarcity, organisms are assumed to behaveas if they maximize their net biomass subject to constraints which express the organisms‘ riskof being preyed upon during predation. Like consumers, organisms face a ‘budget constraint‘requiring their expenditure on prey biomass not to exceed their revenue from supplying ownbiomass. Short-run ecosystem equilibria are defined and derived. The net biomass acquired bythe representative organism in the short term determines the positive or negative populationgrowth. Moving short-run equilibria constitute the dynamics of the predator-prey relationsthat are characterized in numerical analysis. The population dynamics derived here turn out todiffer significantly from those assumed in the standard Lotka-Volterra model.

JEL Code: Q20.

Keywords: organism, biomass, species, population, predator-prey dynamics.

Thomas EichnerUniversity of Siegen

Department of EconomicsHoelderlinstr. 357068 Siegen

[email protected]

Rüdiger PethigUniversity of Siegen

Department of EconomicsHoelderlinstr. 357068 Siegen

[email protected]

The authors gratefully acknowledge financial support by the Deutsche Forschungs-gemeinschaft.

Page 3: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

� � ������-�� ����������

��vNQak�W=K�c9e-M^h�TÇY9[ÄbNSUQ�k�c�VfYRS¹nXbNSUQ�WtM^KHVfQ�Sfc9h�VfM^YRKNTÇv�c�ORQzc�j^YRKN_�VfSfc9kNMPVfM^YRKtM^KtVfvNQ�VfvNQ�YRSUQ�VfM^h�c9j�bEYRb��Nj°cInVfM^YRK��NM^YRj^YR_9W>c9KNk�k�c�VfQ���c9h�>VfYÓVfvNQ�TUQ�e-M^K�c9j��YRS���T�Y9[� �Y9V���c�|¹��{H~RoR}�c9KNk��ÇYRjPVfQ�SUSfcZ|¹��{H~9rH}�l���vNQYRSUM^_RM^K�c9j� �Y9V���cIn��ÇYRjPVfQ�SUSfc e-Y=kNQ�j�Y9[zK�c�V��NSfc9j�bNSUQ�k�c�VfYRS¹nXbNSUQ�WÜTdW=TdVfQ�e-TØ|�� c�W���{Hp9m�����j°c9S�� ��{Hp9rH}V��NSUKNQ�kØY���VzVfY��EQÓY9[Çj^M^e-MPVfQ�k�O9c9j��NQÓc9T�c%kNQ�TUh�SUM^b�VfMPORQÓe-Y=kNQ�jc9KNkØMPVLVfvNQ�SUQ�[DYRSUQ�v�c9T��EQ�Q�KØSUQ���KNQ�kM^K TUQ�ORQ�Sfc9j�!c�W=Tt|�� c�W ��{Rs����� !��c9KN_%c9KNk#"�Q�SUQ�VUV£c ��{R{Rs����!c9KHVfSUQ�j^jc9KNk$��YRTUKNQ�S�~9qRq��I}�l%��vNQ&��cInTUM^h'���NM^j^kNM^KN_(�Nj^Y=h��TLY9[VfvNQ�TUQÓe-Y=kNQ�j^T�Y9[ÆVfvNQ& �Y9V���cIn��ÇYRjPVfQ�SUSfcÓVXW=bEQÓc9SUQ�kNM*)0Q�SUQ�KNh�Q�YRS�kNM*)0Q�SUQ�KHVfM°c9jQ,+-��c�VfM^YRKNT�lÇgÇc9h£vZTUbEQ�h�M^Q�T!M^T�SUQ�bNSUQ�TUQ�KHVfQ�k��HW%c�TUM^KN_Rj^QLQ,+-��c�VfM^YRK%h�YRKHV£c9M^KNM^KN_Óc9T�O9c9SUM°c.�Nj^Q�TÇVfvNQzY/�KbEYRb��Nj°c�VfM^YRK-c9KNk>VfvNQabEYRb��Nj°c�VfM^YRKtY9[�MPVfT�bNSUQ�W=T!YRS�bNSUQ�k�c�VfYRSUT�lÇiLQ�KNh�QaVfvNQ�TUQzbNSUQ�k�c�VfYRS¹nXbNSUQ�W-e-Y=kNQ�j^Tc9SUQ%e>c9h�SUY�n¹c9bNbNSUYHc9h£vNQ�TÓM^KÙVfvNQ%TUQ�KNTUQZVfv�c�VÓVfvNQ�WÙV£c.�9Q%bEYRb��Nj°c�VfM^YRKNTÓc9T0��c9TUM^h��NKNMPVfT�Y9[ac9K�c9jPW=TUM^T�l1*YRb��Nj°c�VfM^YRK _RSUY/�Vfv M^T�c9TUT��Ne-Q�k Sfc�VfvNQ�S�Vfv�c9KÙQ���bNj°c9M^KNQ�kÄl#��vNY=YRTUM^KN_ bEYRb��Nj°c�VfM^YRKNT�c9T&��c9TUM^h-Q�K=nkNYR_RQ�KNY��NTLO9c9SUM°c.�Nj^Q�TLc9e-Y��NKHVfT�VfY>kNM^TUSUQ�_Hc9SUkNM^KN_tVfvNQ�VfSfc9KNTfc9h�VfM^YRKNTLY9[]M^KNkNMPO=M^k���c9j�YRSU_Hc9KNM^TUe-T,�N[8c9M^j^TVfY>M^kNQ�KHVfMP[ÂW%VfvNQ�VXW=bEQ�T�c9KNk TUh�c9j^Q�TaY9[VfvNYRTUQ�VfSfc9KNTfc9h�VfM^YRKNTac9KNk kNY=Q�TLKNY9Vzc9KNT2�Q�SaVfvNQ&+-�NQ�TdVfM^YRK c9TVfYtvNY/AVfvNQ�M^KHVfQ�Sfc9h�VfM^YRK�Y9[M^KNkNMPO=M^k���c9j0YRSU_Hc9KNM^TUe-T�VfSfc9KNTUj°c�VfQ�T�M^KHVfYtbEYRb��Nj°c�VfM^YRK%h£v�c9KN_RQ�T�l

��vNQzbNSUQ�TUQ�KHV�b�c9bEQ�S!c9M^e-T�c�V!bNSUY�O=M^kNM^KN_Óc�e-M^h�SUY9[DY��NKNk�c�VfM^YRK-Y9[�bNSUQ�k�c�VfYRS¹nXbNSUQ�W-k�W=K�c9e-M^h�T�M^Kc3�NKNM^kNM^SUQ�h�VfM^YRK�c9jÄ[DY=Y=k h£v�c9M^K4�HW e-Q�c9KNTLY9[]Q�h�YRKNYRe-M^h�e-Q�VfvNY=kNYRj^YR_9WRl���vNQ�TdV£c9SdVfM^KN_-bEYRM^KHVaY9[]Y��NSc9bNbNSUYHc9h£v M^T�VfvNQ�TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e$e-Y=kNQ�j�M^K��vNM^h£v bEYRb��Nj°c�VfM^YRKNT�c9SUQ�h�YRKNTdV£c9KHV�l5��vNQ�SUQ�bNSUQ�nTUQ�KHV£c�VfMPORQ�YRSU_Hc9KNM^TUe-TLc9SUQÓc9TUT��Ne-Q�k VfY6�EQ�v�c�ORQ�c9TLMP[ÆVfvNQ�W e>cI��M^e-M�7�QzVfvNQ�M^SLKNQ�V��NM^YRe>c9TUTLc9TabNSUM^h�QV£c.�9Q�SUTÓT����-8UQ�h�V�VfY c9bNbNSUYRbNSUM°c�VfQ-h�YRKNTdVfSfc9M^KHVfT�l 9 \=M^e-M^j°c9S�c9T�M^KÙe-Y=kNQ�j^T�Y9[�bEQ�Sd[DQ�h�VfjPW h�YRe-bEQ�VfMPVfMPORQQ�h�YRKNYRe-M^Q�Tac-TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne M^TLkNQ���KNQ�k c9Tzc-TdV£c�VfQ'�vNQ�SUQ�c9j^j�YRSU_Hc9KNM^TUe-TLc9SUQe>cI��M^e-M�7�M^KN_�VfvNQ�M^S�KNQ�V:�NM^YRe>c9TUT,��c9KNk;�NM^YRe>c9TUT!kNQ�e>c9KNk Y9[bNSUQ�k�c�VfYRSUT�Q,+-��c9j^T5�NM^YRe>c9TUT�T��NbNbNjPWZY9[bNSUQ�W=T�lÓ\<�Nh£v Q,+-�NM^j^M��NSUM°c-c9SUQÓTUvNY/�KØVfYZQ���M^TdV�l���vNQ�Q,+-�NM^j^M��NSUM��Ne c9j^j^Y=h�c�VfM^YRK�Y9[=�NM^YRe>c9TUTLVfSfc9KNTfc9h�nVfM^YRKNTah�YRe-bNj^Q�VfQ�jPW�kNQ�VfQ�SUe-M^KNQ�TaVfvNQ�KNQ�V!�NM^YRe>c9TUTUQ�TaQ�c9h£v TUbEQ�h�M^Q�T�c9h,+-�NM^SUQ�kØk��NSUM^KN_-VfvNQÓTUvNYRSdVdnXS��NKbEQ�SUM^Y=kÄl(>LQ�V'�NM^YRe>c9TUT�SUQ�bNSUQ�TUQ�KHVfTZ|DbEYRTUMPVfMPORQ�YRS�KNQ�_Hc�VfMPORQ�}aKNQ�V�Y.)0TUbNSUM^KN_ c9KNk vNQ�KNh�Q>bEYRb��Nj°c�VfM^YRKh£v�c9KN_RQ9l�?�vNQ�K VfvNQ�bEYRb��Nj°c�VfM^YRKZh£v�c9KN_RQ�M^T�j^M^K��9Q�k�VfY-VfvNQ�bEYRb��Nj°c�VfM^YRKNT�Vfv�c�Vav�c�ORQ�bNSUQ�O9c9M^j^Q�k c9KNk�9Q�b�V�h�YRKNTdV£c9KHV�k��NSUM^KN_�VfvNQ�bEQ�SUM^Y=k(�NKNkNQ�S�h�YRKNTUM^kNQ�Sfc�VfM^YRK@��c�TUQ,+-�NQ�KNh�QzY9[ÄTUvNYRSdVdnXS��NK-KNQ�VA�NM^YRe>c9TUTUQ�Th�YRKNTdVfMPV���VfQ�T�VfvNQ�bNSUQ�k�c�VfYRS¹nXbNSUQ�WZk�W=K�c9e-M^h�T�lB ×Ä·I©4µI­�¬�´ ­�µ]­�»�­�¨�È�«�µI´³¶8½�¶R¾9©d·�«fÃ�´ µIÈ�«�¶H´ »�¬�·I©d±½�«£Ë�´ ½!´ Ìd©E¶8­�½!©�­�¾�ÍD©U¸X¬�´ Ã�©N»¼ºIµ�¸X¬�´ ­�µ]·�«�¶RÖ�¨�¶D¬=¾9©d©dµ]´ µ�Ã�©U¶D¬�´ È�«£¬�©Uª

´ µ�»¼­�¨�½�«�²N«�µ�«�² ±�¶8´³¶�¾�±�C*«�µIµI­�µ3DFE�GIHJ,KXÊ-LE¨�­�¸�Ï�©d¨«�µ�ª�×�¶�¸�·I´ ¨�·�«�¨8¬ADFE�G�G�â�KXÊH×�¶�¸�·I´ ¨�·�«�¨8¬AD^â�ã�ã�ãIÊHâ�ã�ã�â�K�«�µ�ª�§N©¹¬�·I´ È«�µ�ª�×�¶�¸�·I´ ¨�·�«�¨8¬@D^â�ã�ãME�KXÀ�×Ä·I©U¶8©�«�º�¬�·I­�¨�¶�«�¶�¶8ºI½!©0¬�·�«£¬�­�¨�È�«�µI´³¶8½�¶=½�«£Ë�´ ½!´ Ìd©0µI©¹¬4©dµI©d¨�È�±Æ¨�«£¬�·I©d¨�¬�·�«�µ�µI©¹¬4¾I´ ­�½�«�¶�¶dÀC�­£¿0©dÃ�©d¨UÊ�´ µa­�ºI¨ÄÃ�´ ©d¿ µI©¹¬�©dµI©d¨�È�±�½�«£Ë�´ ½!´ ÌU«£¬�´ ­�µa¸d«�µa¾9©]¸¹­�µ�¶8´³ª�©d¨�©Uª�©UÑ�ºI´ ã«�² ©dµ�¬0¬�­!µI©¹¬�¾I´ ­�½�«�¶�¶0½�«£Ë�´ ½!´ ÌU«£¬�´ ­�µ�ÀN ¶D®°´ »*½�«£Ë�´ ½!´ ÌU«£¬�´ ­�µ-´³¶!«�²³¶8­�«�¯I¯I² ´ ©Uªt¾�±Ó§N©¹¬�·I´ È�D^â�ã�ã�O,K]«�µ�ªtß4´³¸�·IµI©d¨�«�µ�ªt§N©¹¬�·I´ È�D^â�ã�ã�O,K]¾Iº�¬�­�µ�¬�·I©z² ©dÃ�©d²Ä­�»¶8¯9©U¸¹´ ©U¶4¨�«£¬�·I©d¨�¬�·�«�µ�´ µ�ª�´ Ã�´³ª�º�«�²�­�¨�È�«�µI´³¶8½�¶dÀ=×Ä·I©d´ ¨E½!­�ª�©d²³¶Eª�©dÃ�´³«£¬�©�¶8ºI¾�¶D¬�«�µ�¬�´³«�² ² ±Ç»¼¨�­�½ ¬�·I©�¯I¨�©U¶8©dµ�¬E«�¯I¯I¨�­�«�¸�·�À N¸¹­�½!½!­�µÇ»¼©U«£¬�ºI¨�©Ä­�»R«�² ²�¬�·I©U¶8©Ä½!­�ª�©d²³¶�«�¨�©0©UÑ�ºI´ ² ´ ¾I¨�«£¬�´ µIÈ©U¸¹­�¶8±�¶D¬�©d½Ø¯I¨�´³¸¹©U¶N«�µ�ª�¯I¨�´³¸¹©¹®^¬�«�Ï�´ µIȾ9©d·�«fÃ�´ ­�¨�­�µ�¬�·I©Ä¯�«�¨8¬­�»0­�¨�È�«�µI´³¶8½�¶*­�¨]¶8¯9©U¸¹´ ©U¶dÀ�çI­�¨Ç«�µ�­�¯�¬�´ ½!´ Ìd´ µIÈ�«�¯I¯I¨�­�«�¸�·�¨�©d² ±�´ µIÈa­�µ&P*«�¶8·�¾9©d·�«fÃ�´ ­�¨¿�´ ¬�·I­�º�¬Ç¯I¨�´³¸¹©U¶Æ¶8©d©�§N©¹¬�·I´ ÈD^â�ã�ã�O,KXÀ

Page 4: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

?ÙQ!V£c.�9Q�VfvNQ!O=M^Q�2Vfv�c�VÆVfvNQ�SUQLc9SUQ!SUQ�e>c9S���c.�Nj^Q!TUM^e-M^j°c9SUMPVfM^Q�T �EQ�V �Q�Q�K%czh�YRKNT��Ne-Q�S � TÇkNQ�h�M^TUM^YRKbNSUY��Nj^Q�eAM^K�VfvNQÇh�YRKHORQ�KHVfM^YRK�c9j�Q�h�YRKNYRe-M^hÆvNY��NTUQ�vNYRj^k�VfvNQ�YRSdW�c9KNk�c9K�YRSU_Hc9KNM^TUe � T�kNQ�h�M^TUM^YRK�bNSUY��Nj^Q�e l��vNQ�bNSUY��Nj^Q�e [8c9h�Q�k;�HW%VfvNQ�h�YRKNT��Ne-Q�S�M^T!VfYth£vNY=YRTUQ�c9e-YRKN_tc9j^j0h�YRe-e-Y=kNMPVfM^Q�T�Vfv�c�VLc9SUQ�c�O9c9M^j°c.�Nj^Q[DYRSÓb��NSUh£v�c9TUQ M^K VfvNQZe>c9S��9Q�V�l ��vNQ�h�YRKNT��Ne-Q�S � Ttb��NSUh£v�c9TUQ�M^T0��K�c9KNh�Q�k �HW vNQ�S�h�c9bNMPV£c9j�M^KNh�YRe-Qc9KNk4��YRS%j°c.�EYRS>M^KNh�YRe-Q9l \<�NbNbNjPW=M^KN_ j°c.�EYRS>M^T>KNQ�h�Q�TUTfc9SdW [DYRS |De-YRTdV�}th�YRKNT��Ne-Q�SUT%VfY Q�c9SUK VfvNQ�M^Sj^MPO=M^KN_ c9KNk VfvNM^T%M^T%TUM^e-M^j°c9S-M^K h�c9TUQØY9[�YRSU_Hc9KNM^TUe-T6�MPVfv VfvNQ�M^S%T��NbNbNjPW Y9[�Y/�K �NM^YRe>c9TUT�l ��vNQj^M^K�� �EQ�V �Q�Q�K2kNQ�e>c9KNkNM^KN_Øh�YRe-e-Y=kNMPVfM^Q�T�c9KNkÜT��NbNbNjPW=M^KN_Øj°c.�EYRS�M^T�[DYRSUe>c9j^jPW Q�TdV£c.�Nj^M^TUvNQ�kÜM^K VfvNQ���NkN_RQ�Vzh�YRKNTdVfSfc9M^KHV�l��XK VfvNQ�Q�h�YRTdW=TdVfQ�e;�Äc9K YRSU_Hc9KNM^TUe kNQ�e>c9KNkNT:�NM^YRe>c9TUTLY9[]bNSUQ�W=T�c9KNk T��NbNbNj^M^Q�TY/�K �NM^YRe>c9TUTÓVfY bNSUQ�k�c�VfYRSUT�l ��vNQ Q�h�YRj^YR_RM^h�c9j�bNSUQ�k�c�VfM^YRKÜSUM^T���| �M^e>cØc9KNk2`aM�� ��{R{RqH}�T��N_R_RQ�TdVfTVfv�c�V�c9K%YRSU_Hc9KNM^TUe � TÇkNQ�e>c9KNk@��h�c9b�V��NSUQzc9KNkZM^KHV£c.�9QaY9[�bNSUQ�W6�NM^YRe>c9TUT�KNQ�h�Q�TUTfc9SUM^jPW>M^T�h�YRSUSUQ�j°c�VfQ�k>VfYMPVfTaQ���bEYRT��NSUQÓVfYZbNSUQ�k�c�VfYRSUT�c9KNkØvNQ�KNh�Q�KNQ�h�Q�TUTfc9SUM^jPW Q�KHV£c9M^j^TLVfvNQÓTfc9h�SUM*��h�QÓY9[ÇTUYRe-QÓY/�K$�NM^YRe>c9TUT�l�XKHVfSUY=k��Nh�M^KN_%bNSUM^h�Q�T�c9TaTUh�c9SUh�MPVXW M^KNkNM^h�c�VfYRSUTL[DYRSLQ�c9h£vØVXW=bEQÓY9[ �NM^YRe>c9TUT�VfvNQÓbNSUQ�k�c�VfM^YRK SUM^T��ZV£c.�9Q�TVfvNQ [DYRSUe Y9[�c ���NkN_RQ�V�h�YRKNTdVfSfc9M^KHVZSUQ,+-�NM^SUM^KN_ÙVfvNQØQ���bEQ�KNkNMPV��NSUQ�T%[DYRS��NM^YRe>c9TUT>Y9[�bNSUQ�W TUbEQ�h�M^Q�TKNY9V�VfY Q���h�Q�Q�k2VfvNQ M^KNh�YRe-Q>[DSUYRe T��NbNbNjPW=M^KN_ Y/�K �NM^YRe>c9TUT�l ��vNQ SUQ�bNSUQ�TUQ�KHV£c�VfMPORQ YRSU_Hc9KNM^TUe Y9[c�TUbEQ�h�M^Q�T�e>cI��M^e-M�7�Q�T�MPVfT�KNQ�V&�NM^YRe>c9TUT�T����-8UQ�h�V�VfY VfvNQ3���NkN_RQ�V�h�YRKNTdVfSfc9M^KHV�l��XK VfvNM^T�[DSfc9e-Q��YRS��VfvNQtYRSU_Hc9KNM^TUe-T � YRb�VfM^e>c9jkNQ�e>c9KNkNT�c9KNk T��NbNbNj^M^Q�T�h�c9K �EQ�VfvNY��N_RvHV�Y9[�c9T��EQ�M^KN_�h�Y=YRSUkNM^K�c�VfQ�k$�HWbNSUM^h�Q�T�l���v-�NT!c�h�YRKNh�Q�b�V�Y9[Äc�_RQ�KNQ�Sfc9j�TUvNYRSdVdnXS��NK-Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne M^T]b���V�[DYRS2!c9SUk �vNM^h£v>M^TQ,+-�NMPO9c9j^Q�KHVI��M^K%TUbNM^SUMPVI��VfY�VfvNQzKNY9VfM^YRK%Y9[*c�_RQ�KNQ�Sfc9j0bEQ�Sd[DQ�h�VfjPW>h�YRe-bEQ�VfMPVfMPORQaQ�h�YRKNYRe-M^hLQ,+-�NM^j^M��NSUM��Ne l

� jPVfvNY��N_Rv�VfvNQLM^kNQ�c�Y9[ÄbNSUY�O=M^kNM^KN_�c�e-M^h�SUY9[DY��NKNk�c�VfM^YRK�[DYRSÇbEYRb��Nj°c�VfM^YRKÓk�W=K�c9e-M^h�TÇM^TÇKNY9VÇKNQ�c9KNk�TUYRe-QzM^e-bEYRSdV£c9KHV�h�YRKHVfSUM�����VfM^YRKNT!v�c�ORQ�c9j^SUQ�c9k�W6�EQ�Q�K�e>c9kNQ.��KNY9V£c.�NjPW6�*TUh£vNM^SUv�c9SdV�|�~9qRqRqH}�c9KNk1*Q�VfvNM^_Óc9KNk��*TUh£vNM^SUv�c9SdV�|�~9qRq��I} �RVfvNQakNQ�SUMPO9c�VfM^YRK-Y9[�h�YRKNh�SUQ�VfQakNM*)0Q�SUQ�KHVfM°c9j4Q,+-��c�VfM^YRKNT=��c9TUQ�kZYRK-VfvNQTUvNYRSdVdnXS��NK YRb�VfM^e-M�7�c�VfM^YRK bNSUY��Nj^Q�e-TzY9[�SUQ�bNSUQ�TUQ�KHV£c�VfMPORQ-YRSU_Hc9KNM^TUe-TLV��NSUKNT�Y���V�VfY��EQ�kNM��-h,�NjPV�l'�*YY��NS5��KNY/�j^Q�kN_RQ.� 1*Q�VfvNM^_>c9KNk;�*TUh£vNM^SUv�c9SdVÓ|�~9qRq��I}�M^T!VfvNQ�YRKNjPW%b�c9bEQ�S�M^K��vNM^h£v T��Nh£v c�kNM*)0Q�SUQ�KHVfM°c9jQ,+-��c�VfM^YRK M^T�kNQ�SUMPORQ�kÄl � ��vNQ�M^S�kNM*)0Q�SUQ�KHVfM°c9jÆQ,+-��c�VfM^YRK SUQ�j°c�VfQ�TzVfY c�TUM^KN_Rj^Q�TUbEQ�h�M^Q�T�[DYRSzVfvNQtTUbEQ�h�M°c9jh�c9TUQ%Vfv�c�VÓVfvNQZbEYRb��Nj°c�VfM^YRKNT�Y9[ac9j^j�Y9VfvNQ�SÓTUbEQ�h�M^Q�T-c9SUQ%h�YRKNTdV£c9KHV�l�XKÜh�YRKHVfSfc9TdVI�ÇY��NSÓbNSUQ�TUQ�KHV>c9b=nbNSUYHc9h£v Q���vNM��NMPVfTtc K-�Ne0�EQ�S-Y9[a_RQ�KNQ�Sfc9j^M�7�c�VfM^YRKNT�c9KNk2kNM*)0Q�SUQ�KNh�Q�T-Vfv�c�V �M^j^j��EQ kNQ�V£c9M^j^Q�k �EQ�j^Y/�l��vNQte-YRTdV�T����NTdV£c9KHVfM°c9jÆkNQ�O=M°c�VfM^YRK [DSUYRe$Q�c9SUj^M^Q�SzTdV��NkNM^Q�T�h�YRKNTUM^TdVfT�M^K VfSUQ�c�VfM^KN_ZSUQ�bNSUQ�TUQ�KHV£c�VfMPORQtYRS¹n_Hc9KNM^TUe-TÆTUM^e-M^j°c9S�VfY�Q�h�YRKNYRe-M^h!h�YRKNT��Ne-Q�SUT�l ?�vNM^j^Q�iac9KNKNYRK |¹��{Hp9rH} ���*TUh£vNM^SUv�c9SdVa|�~9qRqRq���~9qRqH~R}*c9KNkM^KNKNY.)�c9KNk3�*TUh£vNM^SUv�c9SdV�|�~9qRqRmH}*e-Y=kNQ�j�YRSU_Hc9KNM^TUe-TÇc9TÇQ�h�YRKNYRe-M^h�|DbNSUY=k��Nh�VfM^YRK4}���SUe-T,�<1*Q�VfvNM^_�c9KNk�*TUh£vNM^SUv�c9SdVZ|�~9qRq��I}�c9bNbNjPWØVfvNQ-Q�h�YRKNYRe-M^hth�YRKNh�Q�b�VÓY9[�h�YRKN_RQ�TdVfM^YRK@� �Q�j^j ��KNY/�KÙ[DSUYRe VfvNQ-b����Nj^M^h_RY=Y=kNT]j^MPVfQ�Sfc�V��NSUQ9l ��vNM^T]h�YRKNh�Q�b�V�M^T �Q�j^j�T��NMPVfQ�kt[DYRS]SUQ�TUY��NSUh�QLh�YRe-bEQ�VfMPVfM^YRK0����V�c9bNbEQ�c9SUTÇVfY��EQ�j^Q�TUTc9bNbNSUYRbNSUM°c�VfQz[DYRS�Q���bNj°c9M^KNM^KN_ÓbNSUQ�k�c�VfYRS¹nXbNSUQ�WZSUQ�j°c�VfM^YRKNT�l

��vNQabNSUQ�TUQ�KHV�b�c9bEQ�S�M^TÇYRSU_Hc9KNM�7�Q�k%c9T�[DYRj^j^Y/�T�l]\=Q�h�VfM^YRKZ~�bNSUQ�TUQ�KHVfT�VfvNQaTUvNYRSdVdnXS��NK>Q�h�YRTdW=TdVfQ�ee-Y=kNQ�j��4kNQ�SUMPORQ�TzVfvNQ�TUvNYRSdVdnXS��NKØQ�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne c9KNkØbNSUY�ORQ�T�MPVfTaQ���M^TdVfQ�KNh�Q�Vfv-�NT�c9TUT��NSUM^KN_� ß4´³¸�·IµI©d¨�«�µ�ªL§N©¹¬�·I´ È�D^â�ã�ã�O,KE«�²³¶8­�ª�©d¨�´ Ã�©Æª�´ ÛR©d¨�©dµ�¬�´³«�²R¯9­�¯IºI²³«£¬�´ ­�µa©UÑ�º�«£¬�´ ­�µ�¶0¾Iº�¬Ä¬�·I©d´ ¨�¾�«�¶8´³¸*ºIµI´ ¬�­�»N«�µ�«�² ±�¶8´³¶

«�¨�©]¶8¯9©U¸¹´ ©U¶Ä¨�«£¬�·I©d¨0¬�·�«�µz¨�©d¯I¨�©U¶8©dµ�¬�«£¬�´ Ã�©­�¨�È�«�µI´³¶8½�¶E­�»�¶8¯9©U¸¹´ ©U¶dÀ

~

Page 5: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

Vfv�c�VaY��NS�SUQ�T��NjPVfTzc9SUQ�KNY9VLO9c9h,�NY��NT�l � VLVfvNQ�Q�KNk Y9[]TUQ�h�VfM^YRKØ~0�Q�bEQ�Sd[DYRSUe c-h�YRe-b�c9Sfc�VfMPORQ�TdV£c�VfM^hc9K�c9jPW=TUM^T!VfY-c9KNT2�Q�S�VfvNQ�+-�NQ�TdVfM^YRK c9T!VfYtvNY/AVfvNQ�Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM°cÓc9SUQ�c )0Q�h�VfQ�k4�HWZh£v�c9KN_RQ�TM^KtSUQ�TUY��NSUh�QLQ�KNkNY/�e-Q�KHVfT�c9KNk-bEYRb��Nj°c�VfM^YRKNT�l �XK-TUQ�h�VfM^YRK>m!�Q�V��NSUKtVfY�VfvNQ�_RSUY/�Vfv-Y9[0bEYRb��Nj°c�VfM^YRKNTc9KNk2kNQ�SUMPORQZVfvNQ�kNM*)0Q�SUQ�KHVfM°c9j!Q,+-��c�VfM^YRKNT �vNM^h£v2h£v�c9Sfc9h�VfQ�SUM�7�QZVfvNQ�bNSUQ�k�c�VfYRS¹nXbNSUQ�W k�W=K�c9e-M^h�T�l �XKTUQ�h�VfM^YRKZy&�Q�b�c9Sfc9e-Q�VfSUM�7�QLVfvNQze-Y=kNQ�j��HW���Y����=n¹`aY��N_Rj°c9T�[F�NKNh�VfM^YRKNT�c9KNkZbNSUY�O=M^kNQaVfvNSUQ�QzkNM*)0Q�SUQ�KHVK-�Ne-Q�SUM^h�c9j*TUbEQ�h�M*��h�c�VfM^YRKNTLW=M^Q�j^kNM^KN_-e-YRSUQ�h�YRKNh�SUQ�VfQÓM^K�[DYRSUe>c�VfM^YRK c.�EY���VaVfvNQ�kNQ�ORQ�j^YRbNe-Q�KHV�Y9[]VfvNQbNSUQ�k�c�VfYRS¹nXbNSUQ�W TdW=TdVfQ�e M^K VfM^e-Q9l ��vNQ�bEYRb��Nj°c�VfM^YRK k�W=K�c9e-M^h�T ����������� vNQ�SUQZV��NSUKÜY���V�VfY kNM*)0Q�STUM^_RKNM*��h�c9KHVfjPW-[DSUYRe VfvNYRTUQ ��������� ��� M^KZVfvNQ�TdV£c9KNk�c9SUk; �Y9V���cIn��ÇYRjPVfQ�SUSfcÓe-Y=kNQ�j�l� ��� � ������(Ä %(Ä����& ��� � � � ( � ���*� ���!�Æ&

����� ���! #"#$&%('*)+',"#'�-&.0/1%('�%(2#$3)+"54#.6�!'��YRKNTUM^kNQ�S�c9KÙQ�h�YRTdW=TdVfQ�e Y9[A����Q�k TUM�7�Q |DYRS�TUb�c9h�Q�}�M^K �vNM^h£v87 TUbEQ�h�M^Q�T�[DYRSUe c YRKNQ�nXkNM^SUQ�h�VfM^YRK�c9jKNYRK=nXh�M^SUh,�Nj°c9S�[DY=Y=k h£v�c9M^KÄwL\=bEQ�h�M^Q�T97 [DQ�Q�kNTzYRK TUbEQ�h�M^Q�T97;:=<��0TUbEQ�h�M^Q�T&7>:=<�[DQ�Q�kNTzYRK TUbEQ�h�M^Q�T7?:A@<�CBDBDB �ÆTUbEQ�h�M^Q�T-~�[DQ�Q�kNTÓYRK TUbEQ�h�M^Q�T%���]c9KNk TUbEQ�h�M^Q�T%�>[DQ�Q�kNTÓYRKÜc SUQ�TUY��NSUh�Q%SUQ�[DQ�SUSUQ�k VfYØc9T� TUbEQ�h�M^Q�T!q � M^K-VfvNQ�[DYRSUe>c9j�e-Y=kNQ�j�l�"!c9TUM^h:�NKNMPVfT�Y9[�c9K�c9jPW=TUM^T�c9SUQ�VfvNQLM^KNkNMPO=M^k���c9j�YRSU_Hc9KNM^TUe-TÇY9[ÄQ�c9h£vTUbEQ�h�M^Q�T�l �*Y�TUM^e-bNj^MP[ÂW���c9j^jEYRSU_Hc9KNM^TUe-T�Y9[*YRKNQ�c9KNk%VfvNQzTfc9e-QaTUbEQ�h�M^Q�T�c9SUQ�c9TUT��Ne-Q�k�c9j^M��9Q9l]iLQ�KNh�Q�MPVT�� �-h�Q�T�VfYÓ[DY=h,�NT�YRK�cÓSUQ�bNSUQ�TUQ�KHV£c�VfMPORQ�M^KNkNMPO=M^k���c9jEY9[*Q�c9h£v�TUbEQ�h�M^Q�TFE��*EHG�<JIDBDBDBKI�7 �vNM^h£v��Q�h�c9j^jYRSU_Hc9KNM^TUeLE��N[DYRS�TUvNYRSdV�l

�XK%VfvNQzTUvNYRSdVdnXS��NK%bEQ�SUM^Y=k-VfvNQzbEYRb��Nj°c�VfM^YRKNMPO�Y9[�Q�c9h£v�TUbEQ�h�M^Q�TCEM^T!c9TUT��Ne-Q�k%VfY0�EQah�YRKNTdV£c9KHV�l`aQ�KNY9VfQ:�HWRQSOUTSV]YRSU_Hc9KNM^TUeWE � T�M^KHV£c.�9Q�Y9[@�NM^YRe>c9TUTÇY9[ÄTUbEQ�h�M^Q�TXE�:Y<Ó|DkNQ�e>c9KNk4}]c9KNk6�HWRZ[OEYRSU_Hc9KNM^TUeE � T-j^YRTUT |DYRStTfc9h�SUM*��h�Q�}ÓY9[zY/�K �NM^YRe>c9TUT�\-VfY MPVfTtbNSUQ�k�c�VfYRSUT |DT��NbNbNjPWN}Ók��NSUM^KN_ØVfvNQ bEQ�SUM^Y=k �NKNkNQ�Sh�YRKNTUM^kNQ�Sfc�VfM^YRKÄl ��[4YRSU_Hc9KNM^TUe]EHG�<JIDBDBDBKI�7 h�c9SUSUM^Q�TY���V*VfvNQ�VfSfc9KNTfc9h�VfM^YRK_^QSOUTSV�I�Z[Oa` �9MPVfT*KNQ�V��NM^YRe>c9TUTc9h,+-�NM^SUQ�k M^T

b O6Gdc Ofe QSOUTSVg I�Z[OTHh I |¹�I}

�vNQ�SUQZVfvNQ%[F�NKNh�VfM^YRK�c O M^T�c h�YRKNh�c�ORQ�e>c9bNbNM^KN_ [DSUYReji g]k=l m IonZ[OUp!M^KHVfYqiLl \=M^KNh�Q%YRSU_Hc9KNM^TUerEVfSfc9KNTd[DYRSUe-TLVfvNQ�bNSUQ�W#�NM^YRe>c9TUTsQSOUTSVaM^KHVfY%Y/�K$�NM^YRe>c9TUT,���Q�v�c�ORQNc Ot u m l'� YRSUQ�Y�ORQ�S,�vc Ot�t w mSUQ�x�Q�h�VfT�kNQ�h�SUQ�c9TUM^KN_�e>c9SU_RM^K�c9j=SUQ�V��NSUKNT�lXyzKtVfvNQLY9VfvNQ�SÇv�c9KNk@��c Oz w m �EQ�h�c.�NTUQLY/�K6�NM^YRe>c9TUT ���NM^jPV�Nb(�HW�[DYRSfc9_RM^KN_aM^TÆh�YRKNh�Q�kNQ�ktVfY�bNSUQ�k�c�VfYRSUT�l5c Oz�z{w m M^TÆbNj°c.�NTUM��Nj^Q.�.�EQ�h�c.�NTUQ�_RSUY/�M^KN_�j^YRTUTUQ�T]Y9[EY/�K�NM^YRe>c9TUT�v�c�ORQ�c9K�M^KNh�SUQ�c9TUM^KN_RjPWzTUQ�SUM^Y��NT�KNQ�_Hc�VfMPORQÇM^e-b�c9h�V�YRK�VfvNQÇYRSU_Hc9KNM^TUe � T�Sfc�VfQÇY9[NSUQ�bNSUY=k��Nh�VfM^YRKÄl��vNQ:�NbNbEQ�S �EY��NKNk8nZ[OEYRKtVfvNQ�kNYRe>c9M^K�Y9[6c O M^T]M^KHVfSUY=k��Nh�Q�k3�EQ�h�c.�NTUQ�VfvNQ�SUQ�bNSUQ�TUQ�KHV£c�VfMPORQaYRSU_Hc9KNM^TUeh�c9KNKNY9V%T��NTdV£c9M^K VfvNQ j^YRTUT-Y9[�Y/�K �NM^YRe>c9TUT3�EQ�WRYRKNk TUYRe-Q VfvNSUQ�TUvNYRj^k@��Tfc�WWnZ[O�l � YRSUQ [DYRSUe>c9j^jPW��| çI­�¨0}S~���Ê�������´³¶Ä­�¨�È�«�µI´³¶8½ E�Î ¶Ä´ µ�¬�«�Ï�©­�»�¬�·I©]¨�©U¶8­�ºI¨�¸¹©�À

m

Page 6: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

c O M^Tzc9TUT��Ne-Q�kØVfYZTfc�VfM^Td[ÂWqc O ^ m I�Z[O`sG+c O ^QSOUTSV�IJnZ[O`sGL: < �vNM^h£vØM^e-bNj^M^Q�T,���HWØc9TUT��Ne-b�VfM^YRK@�0VfvNQQ��=VfM^KNh�VfM^YRK�Y9[TUbEQ�h�M^Q�TsEUl#c O M^TLc�bNvHW=TUM^YRj^YR_RM^h�c9jE[F�NKNh�VfM^YRK@�NTUM^e-M^j°c9SÇVfYtVfv�c�V�Q�e-bNj^Y�WRQ�k;�HW�iac9KNKNYRK|¹��{Hp9rH} ����SUY=h�9Q�S�c9KNk��*TUh£vNM^SUv�c9SdV�|¹��{R{H~R}Çc9KNk��*TUh£vNM^SUv�c9SdV�|�~9qRqRqH}�l ��V�c9h�h�Y��NKHVfT�[DYRS�e>c9M^KHVfQ�K�c9KNh�Q.�SUQ�TUbNM^Sfc�VfM^YRKÓc9KNk�e-Q�V£c.�EYRj^M^TUe �vNM^h£v�kNQ�bEQ�KNkNT]b�c9SdVfjPW�YRK�VfSfc9KNTfc9h�VfM^YRKNTÆc9KNk�M^T*b�c9SdVfjPW�M^KNkNQ�bEQ�KNkNQ�KHVY9[*VfSfc9KNTfc9h�VfM^YRKNT�l

�SUYRe c9K Q�h�YRKNYRe-M^TdV � T�bEQ�SUTUbEQ�h�VfMPORQ.�fc O M^T�cZbNSUY=k��Nh�VfM^YRKØ[F�NKNh�VfM^YRK TUM^KNh�Q |Â[DYRS{Z[OXG m }LVfvNQM^KNb���V � �NM^YRe>c9TUTÓY9[&EX:�< � M^TÓVfSfc9KNTd[DYRSUe-Q�kÜM^KHVfY VfvNQ�Y���Vfb���V � �NM^YRe>c9TUTÓY9[&E � l "A��V-Sfc�VfvNQ�SÓVfv�c9Ke>c.��M^KN_>VfvNQ�Q�KHVfM^SUQ�Y���Vfb���V�c�O9c9M^j°c.�Nj^Q�VfYZY9VfvNQ�S�c9_RQ�KHVfT,�*c9TzQ�h�YRKNYRe-M^h&��SUe-T�kNY��ÄYRKNjPW b�c9SdV�Y9[�MPVI�K�c9e-Q�jPW Z[O���M^TtY.)0Q�SUQ�kÜ[DYRS�Vfv�c�Vtb��NSUbEYRTUQ9l ��vNQ SUQ�TdVI�Cc O ^QSOUTSV�I�Z[Oa` ��M^T�VfSfc9KNTd[DQ�SUSUQ�kÜVfY VfvNQ�KNQ��=VbEQ�SUM^Y=k |ÂVfY3�EQ�TUbEQ�h�M*��Q�k [F�NSdVfvNQ�S%�EQ�j^Y/a}�l

� KNY9VfvNQ�SÓTdVfSUM���M^KN_ TUM^e-M^j°c9SUMPVXW#�EQ�V �Q�Q�KÜQ�h�YRTdW=TdVfQ�e-T-c9KNk Q�h�YRKNYRe-M^Q�T�M^T�VfvNQ%Q���M^TdVfQ�KNh�Q�c9KNkVfvNQLSUYRj^Q�Y9[Äh�YRe-e-Y=kNMPVfM^Q�T]c9KNk-VfSfc9KNTfc9h�VfM^YRKNT�l �XK>Q�h�YRTdW=TdVfQ�e-T�VfvNQ:�NM^YRe>c9TUTÇY9[ÄQ�c9h£v>TUbEQ�h�M^Q�T�h�c9K6�EQO=M^Q��Q�k-c9T]czh�YRe-e-Y=kNMPVXW�c9KNktTUY�h�c9K�SUQ�TUY��NSUh�Q�Ta|DK-��VfSUM^Q�KHVfT,�HT��NKNj^M^_RvHVI�.!c�VfQ�SÆQ�Vfh9l³}�l���vNQ�j°c�VUVfQ�SÆc9SUQ�NTUQ�k c9TabNSUM^e>c9SdW�M^KNb���VfT�c9KNk VfvNQ�[DYRSUe-Q�Sac9TzM^KHVfQ�SUe-Q�kNM°c�VfQ�bNSUY=k��Nh�VfT�l!�*Sfc9KNTfc9h�VfM^YRKNTLV£c.�9Q�bNj°c9h�QO=M°c bNSUQ�k�c�VfYRS¹nXbNSUQ�W M^KHVfQ�Sfc9h�VfM^YRKNT3�vNM^h£v YRKNQ e-M^_RvHV>c9j^TUY kNQ�TUh�SUM��EQ c9T>VfSfc9kNQ9l � T%M^K Q�h�YRKNYRe-M^he-Y=kNQ�j^T,�VfSfc9kNQ�SUT�h�c9K �EQ%M^kNQ�KHVfM*��Q�kÄw-VfvNQ�SUQZc9SUQ>VfvNYRTUQ��vNY kNQ�e>c9KNk �NM^YRe>c9TUT�Y9[�Y9VfvNQ�SÓTUbEQ�h�M^Q�T|DbNSUQ�k�c�VfYRSUT£}!c9KNkZVfvNYRTUQ��vNYtT��NbNbNjPW%Y/�K��NM^YRe>c9TUT�|DbNSUQ�W=T£}�l � j^j0YRSU_Hc9KNM^TUe-T�|DY9VfvNQ�S!Vfv�c9KZVfvNQzVfYRbbNSUQ�k�c�VfYRS � TUQ�Q:�EQ�j^Y/a}*VfSfc9kNQ�Y/�K6�NM^YRe>c9TUT[DYRS]bNSUQ�W �NM^YRe>c9TUT�l ��vNQ�VfY9V£c9jNT��NbNbNjPW�Y9[0TUYRe-Q�TUbEQ�h�M^Q�T �|DbNSUQ�WN}0�NM^YRe>c9TUTÓe0�NTdVtQ,+-��c9j!VfvNQ%VfY9V£c9j!kNQ�e>c9KNk [DYRS�Vfv�c�V(�NM^YRe>c9TUTÓYRK VfvNQZb�c9SdVtY9[abNSUQ�k�c�VfYRSUT�l\=M^KNh�Q-e-YRTdV�Q�h�YRTdW=TdVfQ�e h�YRe-e-Y=kNMPVfM^Q�T�c9SUQ-M^K TUvNYRSdV�T��NbNbNjPW��ÆkNQ�e>c9KNkNQ�SUT�h�YRe-bEQ�VfQt[DYRS�VfvNQ�M^S��NTUQM^e-bNjPW=M^KN_�Vfv�c�V�TUv�c9kNY/ bNSUM^h�Q�T�c9SUQ�c�VUV£c9h£vNQ�k�VfY-c9j^jÄY9[*VfvNQ�TUQ�h�YRe-e-Y=kNMPVfM^Q�T�ly��NS�c9bNbNSUYHc9h£v M^T�Q�ORQ�K e-YRSUQtQ���bNj^M^h�MPV�c.�EY���V�VfvNYRTUQ>bNSUM^h�Q�T�l�?ÙQ>c9TUT��Ne-Q-Vfv�c�V�Q�h�YRTdW=TdVfQ�eVfSfc9KNTfc9h�VfM^YRKNT>c9SUQ _��NM^kNQ�k c9KNk �NjPVfM^e>c�VfQ�jPWÙh�Y=YRSUkNM^K�c�VfQ�k �HW2bNSUM^h�Q�T>M^K2e0�Nh£v VfvNQ Tfc9e-Q�!c�W c9TVfSfc9KNTfc9h�VfM^YRKNT-c9SUQ _��NM^kNQ�k �HWÜbNSUM^h�Q�T-M^K2bEQ�Sd[DQ�h�VfjPW h�YRe-bEQ�VfMPVfMPORQ�Q�h�YRKNYRe-M^Q�T�l `aQ�KNY9VfQ4�HW��!OLVfvNQbNSUM^h�Q�Y9[ÇVfvNQ(�NM^YRe>c9TUTzY9[�TUbEQ�h�M^Q�T EFG m ID<JIDBDBDB�I�7ØlRyzSU_Hc9KNM^TUe?E � TzVfSfc9KNTfc9h�VfM^YRKNT�c9SUQ�h�YRKNTdVfSfc9M^KNQ�k�HW%VfvNQ�M^KNQ,+-��c9j^MPVXW

�!O Z[O����!OUTSV(QSOUTSV EHG <JIDBDBDBKI�7�B |�~R}y��HO=M^Y��NTUjPW��4|�~R}�M^TM^TUYRe-YRSUbNvNM^hÇVfY�czTdV£c9KNk�c9SUk�vNY��NTUQ�vNYRj^k0���NkN_RQ�V]h�YRKNTdVfSfc9M^KHV]M^KÓQ�h�YRKNYRe-M^h�e-Y=kNQ�j^T�l��vNQ�Q���bEQ�KNkNMPV��NSUQ��!OUTSV(QSOUTSV�YRK bNSUQ�W;�NM^YRe>c9TUT�e0�NTdV��EQ���K�c9KNh�Q�kØY���VaY9[ÆVfvNQ�YRSU_Hc9KNM^TUe � T�M^KNh�YRe-QQ�c9SUKNQ�k;�HW�T��NbNbNjPW=M^KN_tY/�K;�NM^YRe>c9TUT,���!O Z[O�l

��vNQ>bNSUM^h�Q�T��!O!c9KNk�!OUTSV�kNQ�VfQ�SUe-M^KNQ-vNY/ e0�Nh£v Y/�K �NM^YRe>c9TUT�YRSU_Hc9KNM^TUe3ELKNQ�Q�kNT�VfY Y.)0Q�SVfY%MPVfTzbNSUQ�k�c�VfYRSUTaVfY%b��NSUh£v�c9TUQ-c>_RMPORQ�K c9e-Y��NKHV&QSOUTSVaY9[ÇbNSUQ�W4�NM^YRe>c9TUT�l!��vNQ0���NkN_RQ�V�h�YRKNTdVfSfc9M^KHV|�~R}�SUQ�x�Q�h�VfT-M^K2c TUM^e-bNj^Q�����V-TdVfSfc9M^_RvHVU[DYRS2!c9SUk !c�W �v�c�V-Q�h�YRj^YR_RM^TdVfTÓSUQ�[DQ�S�VfYÙc9TtYRSU_Hc9KNM^TUe E � TbNSUQ�k�c�VfM^YRK SUM^T�� �EVfvNQ�SUM^T���Y9[ �EQ�M^KN_>bNSUQ�WRQ�k$�NbEYRK4�vNM^j^Q�bNSUQ�W=M^KN_ | �M^e>c-c9KNkØ`aM�� ��{R{RqH}�la` �NSUM^KN_VfvNQÓbNSUY=h�Q�TUTzY9[][DYRSfc9_RM^KN_Ø|��b��NSUh£v�c9TUM^KN_ QSOUTSV��}�YRSU_Hc9KNM^TUe E�Q���bEYRTUQ�T�MPVfTUQ�jP[ÆVfY%MPVfTabNSUQ�k�c�VfYRSUT,�Äc9KNk

y

Page 7: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

VfvNQ%e-YRSUQ-bNSUQ�W �NM^YRe>c9TUT�YRSU_Hc9KNM^TUe EzkNQ�e>c9KNkNT�VfvNQ%_RSUQ�c�VfQ�S�M^T�VfvNQ%SUM^T�� Y9[%�EQ�M^KN_ kNQ�ORY��NSUQ�k �HWbNSUQ�kNMPVfYRSUT�l � jPVfvNY��N_Rv Y��NS�e-Y=kNQ�j�M^T�kNQ�VfQ�SUe-M^KNM^TdVfM^h.��|�~R}�h�c9b�V��NSUQ�T�VfvNQ�KNY9VfM^YRKÙVfv�c�V-c�V-c _RMPORQ�KTdV£c�VfQtY9[!TUh�c9SUh�MPVXW |DbNSUM^h�Q�T£}zYRSU_Hc9KNM^TUe?E�e0�NTdV�Tfc9h�SUM*��h�Q�VfvNQte-YRSUQtY/�K �NM^YRe>c9TUTzVfvNQ-_RSUQ�c�VfQ�S�VfvNQc9e-Y��NKHVzY9[]bNSUQ�W#�NM^YRe>c9TUTLMPV:!c9KHVfTzVfY>V£c.�9QÓM^KÄl�� YRSUQ�Y�ORQ�S,��|�~R}Lc9j^TUY>Y.)0Q�SUTaVfvNQ�SUQ�e>c9S���c.�Nj^Q�c9KNk�Q�j^j¼n��NVUVfM^KN_aM^KHVfQ�SUbNSUQ�V£c�VfM^YRK�Vfv�c�V]YRSU_Hc9KNM^TUe E � TÆh�YRTdVÇY9[4TUYRe-Q!_RMPORQ�Ktc9e-Y��NKHVHQSOUTSV*Y9[EbNSUQ�W&�NM^YRe>c9TUT,�M^KÓVfQ�SUe-TÆY9[EY/�K(�NM^YRe>c9TUTTfc9h�SUM*��h�Q�k@�HM^TVfvNQ�vNM^_RvNQ�S,�9VfvNQ�j^Y/�Q�S]bNSUM^h�Q�k�M^TÆMPVfTÆY/�K(�NM^YRe>c9TUTSUQ�j°c�VfMPORQVfY-Vfv�c�VaY9[]bNSUQ�W TUbEQ�h�M^Q�T&Ev:=<Rl��XK Y9VfvNQ�S:�YRSUkNT,�1E � Tah�YRTdVzY9[HQSOUTSVLSUM^TUQ�T5�vNQ�KØbNSUQ�W TUbEQ�h�M^Q�T&Ev:=<�EQ�h�YRe-Q�T!TUh�c9SUh�Q�S�SUQ�j°c�VfMPORQLVfYÓbNSUQ�k�c�VfYRS!TUbEQ�h�M^Q�T�EUl ��vNQ�TUh�c9SUh�Q�S!VfvNQzbNSUQ�W-VfvNQ�e-YRSUQLVfM^e-QLM^T�TUbEQ�KHV[DYRSa[DYRSfc9_RM^KN_Zc%_RMPORQ�K c9e-Y��NKHV�Y9[�bNSUQ�W#�NM^YRe>c9TUT�c9KNkØVfvNQ�j^YRKN_RQ�SzM^TaVfvNQ�Q���bEYRT��NSUQ�VfY�bNSUQ�k�c�VfYRSUT�l��vNQ bNSUM^h�Q�T>SUQ�x�Q�h�VZSUQ�j°c�VfMPORQ TUh�c9SUh�MPVfM^Q�T-Y9[zVfvNQ TUbEQ�h�M^Q�T%M^KHORYRjPORQ�k c9KNk vNQ�KNh�QÜ|�~R}�Q���bNSUQ�TUTUQ�TZVfvNQvHW=bEY9VfvNQ�TUM^TzVfv�c�V�YRSU_Hc9KNM^TUe E � T�bNSUQ�k�c�VfM^YRKØSUM^T�� kNQ�bEQ�KNkNT�YRK �EY9Vfv VfvNQ�c9e-Y��NKHV�Y9[�bNSUQ�W#�NM^YRe>c9TUTM^KHV£c.�9Q.� QSOUTSV��Ec9KNk VfvNQ�SUQ�j°c�VfMPORQ�c.���NKNk�c9KNh�Q�Y9[ÆMPVfTLbNSUQ�W�TUbEQ�h�M^Q�Tzc9TLe-Q�c9T��NSUQ�k#�HW�VfvNQ�bNSUM^h�Q�Sfc�VfM^Y�!OUTSV�� �!O�ly��HO=M^Y��NTUjPW VfvNQ�SUQÓM^T�c>h�YRe-bNj^Q�VfQÓc9K�c9j^YR_9W;�EQ�V �Q�Q�K |�~R}ac9KNk VfvNQÓvNY��NTUQ�vNYRj^k � T����NkN_RQ�V�h�YRK=nTdVfSfc9M^KHV�l���Q�Vzcth�Y��NKHVfQ�SL[8c9h�V���c9j�M^e-bNj^M^h�c�VfM^YRK>Q�e-Q�SU_RQ�T5�vNQ�K �!O � m c9KNk �!OUTSV G m l �XK Vfv�c�VLh�c9TUQYRSU_Hc9KNM^TUeLE]M^T�M^KZVfvNQ�j°c9KNk�Y9[ ��Y=h��c9M^_RK��MPVfv�SUQ�TUbEQ�h�VLVfYtMPVfT�bNSUQ�W�c9KNk@��e-YRSUQ�Y�ORQ�S,�NMPV�h�c9K�Tfc�VfM^Td[ÂW|�~R}!�MPVfvNY���V�c9KHW T��NbNbNjPWÙY9[�Y/�K �NM^YRe>c9TUT�l � TÓTUvNY/�K �EQ�j^Y/ YRSU_Hc9KNM^TUejE �Y��Nj^kÙVfvNQ�KÜh£vNY=YRTUQZ[OfG m �0M^K [8c9h�VI�0M^SUSUQ�TUbEQ�h�VfMPORQÓY9[ÇMPVfTzQ���bEYRT��NSUQÓVfY%SUM^T���VfvNSUY��N_Rv [DYRSfc9_RM^KN_%c9KNkØM^SUSUQ�TUbEQ�h�VfMPORQÓY9[ÇMPVfTY/�KØTUh�c9SUh�MPVXW�^ �!Oa`�l��*Y%bNSUQ�ORQ�KHV�VfvNQÓbNSUQ�k�c�VfM^YRK SUM^T���[DSUYRe O9c9KNM^TUvNM^KN_>M^K TUMPV���c�VfM^YRKNTLY9[�c.���NKNk�c9KHVbNSUQ�W��Q��M^j^j0h�YRe-bNj^Q�e-Q�KHV�|�~R}A�HW>VfvNQ�c9TUT��Ne-b�VfM^YRK%Vfv�c�V�VfvNQ�SUQ�M^T�c9j*!c�W=T�c�e-M^KNM^e0�Ne bNSUQ�k�c�VfM^YRKSUM^T�� Vfv�c�V�M^KNh�SUQ�c9TUQ�T �MPVfv VfvNQZM^KHV£c.�9QZY9[LbNSUQ�W �NM^YRe>c9TUTÓM^KNkNQ�bEQ�KNkNQ�KHVtY9[abNSUM^h�Q�T�l ��vNQ�TUM^e-bNj^Q�TdVbEYRTUTUM��Nj^Qz[DYRSUe>c9j^M�7�c�VfM^YRK-Y9[*VfvNM^T�c9TUT��Ne-b�VfM^YRK�M^T

Z[O ����OUQSOUTSV EHG <JIDBDBDBKI�7 |8mH}

�vNQ�SUQ���OÆM^TLM^KHVfQ�SUbNSUQ�VfQ�k c9TLVfvNQ�j^YRTUTÓ|�� T��NbNbNjPWN}�Y9[#E � TaY/�K$�NM^YRe>c9TUT�bEQ�S �NKNMPVaY9[ÇbNSUQ�W;�NM^YRe>c9TUTh�c.�N_RvHVL|�� kNQ�e>c9KNk4} �Hc9KNk�VfvNM^Tj^YRTUTY=h�h,�NSUTÆM^SUSUQ�TUbEQ�h�VfMPORQ�Y9[ �vNQ�VfvNQ�S �!OUTSV#G m YRS �!OUTSV u m lÆiLQ�KNh�Q��O u m Q���bNSUQ�TUTUQ�TaVfvNQ�Q��=VfQ�KHVaVfY(�vNM^h£v YRSU_Hc9KNM^TUe;E�M^T�Q���bEYRTUQ�k VfY-bNSUM^h�Q�nXM^KNkNQ�bEQ�KNkNQ�KHVabNSUQ�k�c�VfM^YRKSUM^T��4l �SUYRe VfvNQ YRSU_Hc9KNM^TUe � T�bEYRM^KHVtY9[aO=M^Q���OLM^T-c h�YRKNTdV£c9KHV>j^M��9Q�c9j^j!bNSUM^h�Q�T�l "A��V%c9T �M^j^j��EQkNM^TUh,�NTUTUQ�k M^KZVfvNQ�KNQ��=VLTUQ�h�VfM^YRK@���O �M^j^j �EQ�Q�KNkNYR_RQ�KNY��NTUjPWZkNQ�VfQ�SUe-M^KNQ�k�M^K�Q,+-�NM^j^M��NSUM��Ne ly��HO=M^Y��NTUjPW���e-Q�e0�EQ�SUT�Y9[�VfvNQ vNM^_RvNQ�TdV Sfc9K���M^KN_2bNSUQ�k�c�VfYRS�TUbEQ�h�M^Q�T,� 7$��kNY2KNY9V [8c9h�QÙc9KHWbNSUQ�k�c�VfM^YRK-SUM^T���TUM^KNh�Q�VfvNQ�W-kNY�KNY9V�v�c�ORQaK�c�V��NSfc9j4Q�KNQ�e-M^Q�T=�HW>c9TUT��Ne-b�VfM^YRKÄl �XK%Y��NS][DYRSUe>c9j�e-Y=kNQ�j��e-Q�e0�EQ�SUT�Y9[�VfvNQ>vNM^_RvNQ�TdV�Sfc9K���M^KN_ bNSUQ�k�c�VfYRS�TUbEQ�h�M^Q�T 7 SUQ,+-�NM^SUQ>TUbEQ�h�M°c9j]VfSUQ�c�Vfe-Q�KHV0�EQ�h�c.�NTUQZc�VVfvNM^T�Q�j^Q�e-Q�KHV�VfvNQ�[DY=Y=kZh£v�c9M^K M^T�c9S��NMPVfSfc9SUM^jPW-h,��VLY.)l � jPVfvNY��N_RvZVfvNQ�e-Y=kNQ�jÄh�YRKHV£c9M^KNT�KNYtkNQ�e>c9KNk[DYRS3�NM^YRe>c9TUT-Y9[�TUbEQ�h�M^Q�T 7 �Q4�M^j^j�Q��=VfQ�KNk VfvNQ h�YRKNTdVfSfc9M^KHVØ|8mH}ÓVfY E Gr7 M^e-bNjPW=M^KN_YZ�� u m�vNQ�KNQ�ORQ�S Q �#TSV u m l � � YRSUQ�Y�ORQ�S,���Q c9TUT��Ne-Q ��� � m c9KNk2h�YRKNTdV£c9KHVZc9KNk2M^KHVfQ�SUbNSUQ�VfQ ���XZ��� ÁµZ¨�©U«�²�©U¸¹­�¶8±�¶D¬�©d½�¶!­�¨�È�«�µI´³¶8½�¶!­�»Æ¬�·I©�¶8¯9©U¸¹´ ©U¶�«£¬�¬�·I©�¬�­�¯Z­�»Æ¬�·I©�»¼­�­�ªZ¸�·�«�´ µZª�­tª�´ ©�Ê�«�¨�©z©U«£¬�©dµZ¾�±t¬�·I©

o

Page 8: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

c9T�YRSU_Hc9KNM^TUe?7 � T�M^KNh�YRe-QÓ[DSUYRe �Q���bEYRSdVfM^KN_ Z��Òc�V �YRSUj^k e>c9S��9Q�V�bNSUM^h�Q ���al �XKHV��NMPVfMPORQ�jPW�� ��OVfQ�KNkNT!VfYÓkNQ�h�SUQ�c9TUQ��MPVfv%M^KNh�SUQ�c9TUM^KN_ EÆTUM^KNh�QaVfvNQzvNM^_RvNQ�S!c�TUbEQ�h�M^Q�T!M^K>VfvNQa[DY=Y=k>h£v�c9M^K%VfvNQzj^Q�TUT�MPV!M^Th£v�c9j^j^Q�KN_RQ�k(�HW�bNSUQ�kNMPVfYRSUT�l]iLQ�KNh�Q � � �M^j^j�bNSUY���c.�NjPW0�EQ�TUe>c9j^j�� ���XZ�� �M^j^j��EQ�TUe>c9j^jNc9KNktTUY��M^j^j��EQVfvNQ�bNSUQ�W�M^KHV£c.�9Q Q �#TSV�l � SU_���c.�NjPW��NVfvNM^T�M^T�KNY9Vzc�[F�Nj^jPW%Tfc�VfM^Td[8c9h�VfYRSdWZkNQ�TUh�SUM^b�VfM^YRK Y9[VfvNQ�bEY/�Q�Sd[F�NjbEYRTUMPVfM^YRKZY9[Æc�vNM^_Rv�Sfc9K���M^KN_tbNSUQ�k�c�VfYRS�l �

iac�O=M^KN_ TUbEQ�h�M*��Q�k YRSU_Hc9KNM^TUe E � TÓh�YRKNTdVfSfc9M^KHVfT'�Q%KNY/ V��NSUKÙVfY MPVfT�kNQ�h�M^TUM^YRKÙbNSUY��Nj^Q�e l�?ÙQc9TUT��Ne-Q�Vfv�c�VLc9j^jÄM^KNkNMPO=M^k���c9j0YRSU_Hc9KNM^TUe-T��EQ�v�c�ORQ�c9T�MP[�VfvNQ�WZTUYRjPORQ�VfvNQ�e>cI��M^e-M�7�c�VfM^YRK>bNSUY��Nj^Q�e w �

������ t��� �� z��� c O ^QSOUTSV�I�Z[O` T�l V�l |�~R}!c9KNk |8mH}�l |Dy�}

�*Y�Y��NS ��KNY/�j^Q�kN_RQ.�RVfvNQ�vHW=bEY9VfvNQ�TUM^T]Y9[ � c9T]MP[ � e>cI��M^e-M�7�c�VfM^YRK�M^Ktc9K�Q�h�YRTdW=TdVfQ�e v�c9T���SUTdV �EQ�Q�KtT��N_�n_RQ�TdVfQ�ktc9KNkÓQ�e-bNj^Y�WRQ�kÓM^K�[DYRSUe>c9j�c9K�c9jPW=TUM^T��HWÓiac9KNKNYRK�|¹��{Hp9rH}�c9KNkÓv�c9TTUM^KNh�QA�EQ�Q�K �NTUQ�k�M^K�TUQ�ORQ�Sfc9jY9VfvNQ�S�TdV��NkNM^Q�T�l �YRS�MPVfT�e-Y9VfMPO9c�VfM^YRK c9KNk Sfc�VfM^YRK�c9j^M�7�c�VfM^YRK TUQ�Q.�]Q9l _Nl*�ÆiLM^SUTUvNj^Q�MP[DQ�S>|¹��{HpRpR} � M^KNKNY.)c9KNk �*TUh£vNM^SUv�c9SdV |�~9qRqRmH}�c9KNk �*TUh£vNM^SUv�c9SdV |�~9qRqRq���~9qRqH~R}�l,y��NStc9bNbNSUYHc9h£v2kNQ�O=M°c�VfQ�TtTUM^_RKNM*��h�c9KHVfjPW[DSUYRe bNSUQ�O=M^Y��NT!TdV��NkNM^Q�T�SUQ�_Hc9SUkNM^KN_�VfvNQah�YRKNTdVfSfc9M^KHVfT�|�~R}Çc9KNk |8mH}�l � T=�Qzv�c�ORQzY���Vfj^M^KNQ�k>c.�EY�ORQaVfvNQYRSU_Hc9KNM^TUe � TzYRb�VfM^e-M�7�c�VfM^YRK bNSUY��Nj^Q�e |Dy�}LM^TzORQ�SdW TUM^e-M^j°c9S�VfYZVfvNQ�Q�h�YRKNYRe-M^h�vNY��NTUQ�vNYRj^k � T�bNSUY��Nj^Q�eY9[�e>cI��M^e-M�7�M^KN_���VfM^j^MPVXWÓT����-8UQ�h�V!VfY�vNM^TÇYRS�vNQ�SA���NkN_RQ�V�h�YRKNTdVfSfc9M^KHV�l �XKZc9K�c9j^YR_9W���c O ^�� `Æh�YRSUSUQ�TUbEYRKNkNTVfYÓVfvNQ�h�YRKNT��Ne-Q�S � T%��VfM^j^MPVXWtkNQ�SUMPORQ�kZ[DSUYRe VfvNQ�c9e-Y��NKHVCQSOUTSV�Y9[cÓh�YRKNT��Ne-Q�S!_RY=Y=kZkNQ�e>c9KNkNQ�k�c9KNkVfvNQ c9e-Y��NKHVNZ[OLY9[zj°c.�EYRS�T��NbNbNj^M^Q�kÄl >LY9VfQ.��vNY/�Q�ORQ�S,��Vfv�c�V-M^K2h�YRKNT��Ne-Q�S-h£vNYRM^h�Q e-Y=kNQ�j^T�j^Y/�Q�S�EY��NKNkNTÓYRK j°c.�EYRS�T��NbNbNjPWÙT��Nh£v2c9T�|8mH}�c9SUQ6�NK���KNY/�K c9KNk Vfv�c�VÓM^KÙVfvNQ%bNSUQ�TUQ�KHV-b�c9bEQ�S c O ^�� `�M^TbNvHW=TUM^h�c9j��NM^YRe>c9TUT�� ���D� ��� ��� Sfc�VfvNQ�S�Vfv�c9K>M^KHV£c9KN_RM��Nj^Q5��VfM^j^MPVXWÓ_RQ�KNQ�Sfc�VfQ�k%M^K-VfvNQah�YRKNT��Ne-Q�S � T!e-M^KNkÄlyzSU_Hc9KNM^TUe-TLc9SUQ�VfvNQ�SUQ�[DYRSUQ�VfSUQ�c�VfQ�kØc9T � vNQ�SUe>c9bNvNSUY=kNMPVfQ�T � M^K VfvNQ�TUQ�KNTUQ�Vfv�c�VaVfvNQ�W c9SUQ�h�YRKNT��Ne-Q�SUTSUQ�_Hc9SUkNM^KN_ÓVfvNQ�M^S%���NkN_RQ�V�h�YRKNTdVfSfc9M^KHV5����VLbNSUY=k��Nh�Q�SUT�SUQ�_Hc9SUkNM^KN_ÓVfvNQ�M^S�bNSUY=k��Nh�VfM^YRKZY9[KNQ�V5�NM^YRe>c9TUTc9h�h�YRSUkNM^KN_�VfY(�NM^YRj^YR_RM^h�c9jÆ|DSfc�VfvNQ�S!Vfv�c9K Q�KN_RM^KNQ�Q�SUM^KN_�}=�Nj��NQ�bNSUM^KHVfT�l

��vNQ%TUYRj���VfM^YRK VfY VfvNQ%M^KNkNMPO=M^k���c9j]YRb�VfM^e-M�7�c�VfM^YRK bNSUY��Nj^Q�e |Dy�}�W=M^Q�j^kNT�kNQ�e>c9KNk c9KNk T��NbNbNjPW[F�NKNh�VfM^YRKNT!Vfv�c�V5�M^j^jEV��NSUK Y���V�VfYtkNQ�bEQ�KNk YRK�bNSUM^h�Q�T�lA� YRSUQ�TUbEQ�h�M*��h�c9j^jPW����Q�M^K�[DQ�S

����� ���"!$#&%�#'�"(*),+ -/. �0� �N����� ��� �N��1 � ��1 � ���2�3�"4�5768 �[�:9��� 1;1 � 1�<�1 �=9 ��> ��� � ��� � � � �!OUTSV ��1 � �!O_��1 � E G <JIDBDBDBKI�7?>&@ � ��� �N��1 � ��1 � ���2�3�"4�5 ��A�[�09 ��1 � ���+E{� ���ª�©U¸¹­�½!¯9­�¶8©d¨�¶Ä«�µ�ªL´ µa¬�·�«£¬*¶8©dµ�¶8©¬�·I©d±�¬�­�­�«�¨�©Æ¯I¨�©d±�ÀB N µL«£¬8¬�¨�«�¸X¬�´ Ã�©Ä¿Ä«f±�­�º�¬4´³¶�¬�­Ç©dµ�ª�­£¿>­�¨�È�«�µI´³¶8½DC2¿�´ ¬�·�¶8­�½!©�©¹Ë�¬�¨�«Æ¯IºI¨�¸�·�«�¶8´ µIÈƯ9­£¿0©d¨UÊ�µ�«�½!©d² ±�¬�·I©�¨�©dÃ�©dµ�ºI©U¶

»¼¨�­�½ ¶8©d² ² ´ µIÈƬ�·I©*¨�©U¶8­�ºI¨�¸¹©�Ê�EGF�HI F7J�KMLÇÊ�¶8­Æ¬�·�«£¬0­�¨�È�«�µI´³¶8½DC�Î ¶4¾Iº�ª�È�©¹¬0¸¹­�µ�¶D¬�¨�«�´ µ�¬4¿0­�ºI²³ª�¾9©*È�´ Ã�©dµ!¾�±ON EGFGHI F7J�KMLQP$RE�L I LTSUE�Lv��� ��Lv���£À�ÉZ´ ¬�·�¬�·I´³¶�¾Iº�ª�È�©¹¬¸¹­�µ�¶D¬�¨�«�´ µ�¬�­�µI©�¸¹­�ºI²³ª�«�¶�¶8ºI½!©VE�LXWZY�«�µ�ª\[�LDWZY!¬�­�¬�·I©�©¹ÛR©U¸X¬�¬�·�«£¬¿�´ ¬�·]EGF�^_YÇ­�¨�È�«�µI´³¶8½`C ¿0­�ºI²³ª�¾9©Æ«�¾I² ©�¬�­�¯IºI¨�¸�·�«�¶8©�¯I¨�©d±!¿�´ ¬�·I­�º�¬�¶8ºI¯I¯I² ±�´ µIÈ�­£¿�µ�¾I´ ­�½�«�¶�¶dÀ�C�­£¿0©dÃ�©d¨UÊ�¬�­�©U«�¶8©¬�·I©L©¹Ë�¯9­�¶8´ ¬�´ ­�µ�ÊN¿0©�¿�´ ² ²Ä¶D¬�´³¸�Ï�¬�­�¬�·I©a«�¶�¶8ºI½!¯�¬�´ ­�µÓ¬�·�«£¬�D¼´ KVE�La^bY�«�µ�ªt¸¹­�µ�¶D¬�«�µ�¬�«�µ�ª�D¼´ ´ K]¬�·�«£¬�­�¨�È�«�µI´³¶8½aC¸d«�µIµI­�¬�ª�´³¶8¯9­�¶8©Æ­�»�«�µ�±�¨�©U¶8­�ºI¨�¸¹©´ µ�¸¹­�½!©�Àc Ô�´ µ�¸¹©ed � N�������7f0YgP ~:d � N�������7fhHI �iP ~Xj5�*¬�·I©Ç¶8­�² º�¬�´ ­�µa¿�´ ² ²=¶�«£¬�´³¶D»¼± I ��kTHI �8À

r

Page 9: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

- � 6�Q��OUTSV G�Q��OUTSV�� G ����e����� t��� c O ^QSOUTSV�I ��OUQSOUTSV�`R��1 � Z�O G ��OUQ��OUTSV A$�[� ��4&4 � ��� � � � >&@!��> �M� 1 � >�D��> � � A 5 �!OUTSV u �!O ��O u m��- �� 6�Q��OUTSV G Q� OUTSV � G ����]����� t��� c O�� QSOUTSV�I�� ��� � QSOUTSV� ��1 � Z�O G+^ �!OUTSV � �!O` Q� OUTSV�� � A �!OUTSV ���!O ��O um��� j^jzbNSUYRbEYRTUMPVfM^YRKNT�c9SUQ bNSUY�ORQ�kAM^K�VfvNQ c9bNbEQ�KNkNM¼�0l � h�h�YRSUkNM^KN_ÜVfY2bNSUYRbEYRTUMPVfM^YRK �Ø[DYRS c9KHW�h�YRK=nTdVfQ�j^j°c�VfM^YRK�Y9[ÓbNSUM^h�Q�T�VfvNQÙkNQ�e>c9KNk=Q��OUTSV M^T�Q,+-��c9j�VfY Q�MPVfvNQ�S_Q��OUTSV YRS Q� OUTSV l �XKÕ[8c9h�VI���QÙv�c�ORQQ��OUTSV G ������� Q��OUTSV I Q� OUTSV�� l��*Y TUQ�Q-VfvNQ>SUQ�c9TUYRK [DYRS�VfvNM^T�SUQ�T��NjPV�T��NbNbEYRTUQ3��SUTdV�Vfv�c�V�c9j^j]bNSUM^h�Q�T�c9SUQTdVfSUM^h�VfjPW%bEYRTUMPVfMPORQ9l ��vNQ�K YRSU_Hc9KNM^TUeLE][8c9h�Q�T�VfvNQ�h�YRKNTdVfSfc9M^KHVsZ[O����SOUTSV(QSOUTSV�c9KNk Z[O ����O QSOUTSVA�vNQ�SUQ�SOUTSV � G �!OUTSV�� �!O�c9SUQ-VfvNQ-VfQ�SUe-T�Y9[�VfSfc9kNQ9l#��j^Q�c9SUjPW��*VfvNQ>h�YRKNTdVfSfc9M^KHV�|�~R}�� h�YRKNTdVfSfc9M^KHV�|8mH}� �M^T�KNY9V�NM^KNkNM^KN_>MP[!�SOUTSV w ��O"� �SOUTSV u ��O� TUM^KNh�Q�[DYRSzc9KHW�^QSOUTSV�I�Z[Oa`%�MPVfv QSOUTSV u m Tfc�VfM^Td[ÂW=M^KN_ Z[OHG ��O QSOUTSV� Z[O6G��SOUTSV(QSOUTSV# �Q�KNQ�h�Q�TUTfc9SUM^jPW>_RQ�VFZ[O u �SOUTSV(QSOUTSV$� Z[O u ��OUQSOUTSV# �l M^_��NSUQ���M^j^j��NTdVfSfc�VfQ�TÇVfvNQ�h�YRKNTUQ�n+-�NQ�KNh�Q�T][DYRSYRSU_Hc9KNM^TUe E � T]YRb�VfM^e>c9j�bNj°c9KÄl���vNQ�TdVfSfc9M^_RvHVÆj^M^KNQ�T m �&%OUTSV � m ��O4c9KNk m �&'OUTSV c9SUQ�VfvNQ!_RSfc9bNvNTY9[VfvNQ�j^M^KNQ�c9S![F�NKNh�VfM^YRKNTsZ[O0G(�&%OUTSV QSOUTSV�� Z[O G ��OUQSOUTSVLc9KNk Z[O G(�&'OUTSV QSOUTSV��4SUQ�TUbEQ�h�VfMPORQ�jPW��ETfc�VfM^Td[ÂW=M^KN_�&%OUTSV u ��O u �&'OUTSV l ��[�VfvNQLSUQ�j°c�VfMPORQLbNSUM^h�Q"�&'OUTSV bNSUQ�O9c9M^j^T,�HVfvNQaYRSU_Hc9KNM^TUe �Y��Nj^k%j^M��9Q�VfY�h£vNY=YRTUQabEYRM^KHV) M^K ��_��NSUQ��:����V�M^TÆ[DYRSUh�Q�ktVfY�h£vNY=YRTUQLbEYRM^KHVXcÒTUM^KNh�Q�|8mH}M^TÇe-YRSUQ�SUQ�TdVfSUM^h�VfMPORQ�Vfv�c9K |�~R}Æc9KNk-vNQ�KNh�Q|8mH}aM^TzVfvNQtYRKNjPW#�NM^KNkNM^KN_Zh�YRKNTdVfSfc9M^KHV�l3��YRKHORQ�SUTUQ�jPW��c�V�SUQ�j°c�VfMPORQÓbNSUM^h�Q*�&%OUTSV � Z[O �+�&%OUTSV QSOUTSVzM^TzVfvNQ�NM^KNkNM^KN_Óh�YRKNTdVfSfc9M^KHV�c9KNkZh�YRKNTUQ,+-�NQ�KHVfjPW%VfvNQzYRSU_Hc9KNM^TUe M^T�[DYRSUh�Q�kZVfYÓh£vNY=YRTUQ�bEYRM^KHV-, |DSfc�VfvNQ�S�Vfv�c9Kc�}�l

�XK VfQ�SUe-T�Y9[ÆbNSUQ�k�c�VfM^YRK SUM^T�� ��VfvNQ�M^KHVfQ�SUbNSUQ�V£c�VfM^YRK�M^T�TdVfSfc9M^_RvHVU[DYRS2!c9SUkÄl ��[]YRSU_Hc9KNM^TUeLE � TLbNSUQ�WTUbEQ�h�M^Q�T E5:]<>M^T�SUQ�j°c�VfMPORQ�jPWØc.���NKNk�c9KHV ^.�SOUTSV0/ ��Oa` �HE � T�Q���bEYRT��NSUQ-VfY MPVfT�Y/�KÙbNSUQ�k�c�VfYRSUT�k��NSUM^KN_[DYRSfc9_RM^KN_%M^KNh�SUQ�c9TUQ�T��MPVfvØVfvNQ-c9e-Y��NKHV�Y9[�bNSUQ�W M^KHV£c.�9Q9l("A��V��vNQ�K1�SOUTSV u ��O�YRSU_Hc9KNM^TUe E�KNQ�Q�kNTe-YRSUQ�VfM^e-Q�VfYÓTUQ�c9SUh£v%[DYRSz|DQ�c9h£v��NKNMPV!Y9[£}]bNSUQ�W%c9KNk%vNQ�KNh�Qzh�c9SUSUM^Q�T!c�_RSUQ�c�VfQ�S�SUM^T��tY9[ �EQ�M^KN_ÓbNSUQ�WRQ�k�NbEYRK k��NSUM^KN_Ó[DYRSfc9_RM^KN_Nl

��vNQ>c9SU_��Ne-Q�KHV�Y9[�|�~R}�c9KNk |8mH}��EQ�M^KN_�e0��V���c9j^jPW Q���h�j��NTUMPORQ-h�YRKNTdVfSfc9M^KHVfT�h�c9K �EQ-Q�c9TUM^jPW Q���nVfQ�KNkNQ�k2VfY h�Y�ORQ�S37�Q�SUY bNSUM^h�Q�T�l ��[ ��[DYRS�Q��Nc9e-bNj^Q.�2�SOUTSV G m �ÇVfvNQ�j^M^KNQ_Z[O G3�SOUTSV(QSOUTSV�h�YRM^KNh�M^kNQ�T�MPVfv VfvNQ�c.�NTUh�M^TUTfc%M^K#��_��NSUQ%�Rl�\=M^KNh�Q���O u �SOUTSV&G m �EVfvNQ�YRSU_Hc9KNM^TUe � T �EQ�TdV�h£vNYRM^h�QÓM^TaVfvNQÓbEYRM^KHVc>l �XKÙY9VfvNQ�S��YRSUkNT,�HE�h£vNY=YRTUQ�T Q��OUTSV |DbEYRM^KHV c�}a[DYRS�c9KHW4�SOUTSV65 l m I ��OUp���Vfv�c�V�M^T,� E�M^T�M^KNkNM*)0Q�SUQ�KHV�MPVfv SUQ�TUbEQ�h�VzVfY-bNSUM^h�Q�h£v�c9KN_RQ�T:�MPVfvNM^K�Vfv�c�VaM^KHVfQ�SdO9c9j�l!` �NQ�VfYtVfvNM^TLY��NTUQ�SdO9c�VfM^YRK YRKNQ�h�Y��Nj^k V£c.�9Q��O u m c9Tac-j^Y/�Q�S:�EY��NKNk Y9[7�SOUTSV�[DYRSac9j^j0E#G+<JIDBDBDBKI�7L:=<Rl5>LY9VfQ.�4vNY/�Q�ORQ�S,�0Vfv�c�V �HW kNQ���KNMPVfM^YRKY9[8��9FG+^ ��9 � �1V ` �:�6VXG+^ �1V � ��;�`!Q�Vfh9l*���SOUTSV ����O*TUM^e0�NjPV£c9KNQ�Y��NTUjPW%Q�TdV£c.�Nj^M^TUvNQ�TLc9K;�NbNbEQ�S5�EY��NKNk YRKc9j^j7�SOUTSV�l���vNQ�TUQ6�EY��NKNkNT�h�YRKNTdVfMPV���VfQ>c9kNkNMPVfM^YRK�c9j ��c9SUSUM^Q�SUT�VfY VfvNQtTUe-Y=Y9Vfv �YRS���M^KN_ Y9[!VfvNQ-bNSUM^h�Qe-Q�h£v�c9KNM^TUe h�SUQ�c�VfM^KN_>bNSUY��Nj^Q�e-T�M^K Q�TdV£c.�Nj^M^TUvNM^KN_tVfvNQ�Q���M^TdVfQ�KNh�QÓY9[]Q,+-�NM^j^M��NSUM��Ne lA��vNM^TLM^T5�vHW��QSUQ�[DSfc9M^KZ[DSUYRe M^KHVfSUY=k��Nh�M^KN_ÓVfvNQ�h�YRKNTdVfSfc9M^KHVfT-�SOUTSV ����O�[DYRS�c9j^j1EHG�<JIDBDBDB�I�7L: <Rl

��YRKNTUM^kNQ�SÓKNY/ VfvNQ%h�c9TUQ>Vfv�c�V Q��OUTSV G>Q� OUTSV G ����e����� t��� c O ^QSOUTSV�I�SOUTSV QSOUTSV�`�c9KNk�Z�O G�SOUTSV(Q��OUTSV l(��vNQ�K VfvNQte>cI��M^e0�Ne$Y9[�c O ^�� ` �MPVfv SUQ�TUbEQ�h�V�VfY_QSOUTSVzM^T�Y��HO=M^Y��NTUjPW h£v�c9Sfc9h�VfQ�SUM�7�Q�k �HWp

Page 10: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

M^_��NSUQ��RwXyzSU_Hc9KNM^TUeLE � T�YRb�VfM^e>c9j0kNQ�e>c9KNk c9KNk T��NbNbNjPWVfvNQ!��SUTdVdnXYRSUkNQ�S�h�YRKNkNMPVfM^YRK

: c Ot�� Q��OUTSV I�Z�O��c Oz�� Q �OUTSV I�Z �O � G �SOUTSV [DYRS_EHG�<JIDBDBDB�I�7�B� T���KNY/�K [DSUYRe VfQ��=V��EY=Y��2h�YRKNT��Ne-Q�S-VfvNQ�YRSdW2VfvNM^T>Q,+-��c�VfM^YRK SUQ,+-�NM^SUQ�T%YRSU_Hc9KNM^TUe E�VfY Q���b�c9KNkVfvNQØM^KHV£c.�9QØY9[�bNSUQ�W �NM^YRe>c9TUT,��QSOUTSV���VfY VfvNQØbEYRM^KHVZc�V��vNM^h£v :&c Ot �c Oz ��VfvNQØe>c9SU_RM^K�c9j�Sfc�VfQØY9[T����NTdVfMPV���VfM^KN_�Y/�K �NM^YRe>c9TUTz[DYRS�bNSUQ�W �NM^YRe>c9TUT,��Q,+-��c9j^T�VfvNQ |DQ��=VfQ�SUK�c9jÂ}zSfc�VfQtY9[�Q���h£v�c9KN_RM^KN_ Y/�K�NM^YRe>c9TUTÓ[DYRStQ�c9h£v �NKNMPVtY9[abNSUQ�W �NM^YRe>c9TUT�l ��[&Q��OUTSV G?Q��OUTSV �=�Q _RQ�Vq^(:&c Ot �c Oz ` G ��O5�MPVfv2c9KM^KHVfQ�SUbNSUQ�V£c�VfM^YRK�c9K�c9j^YR_RY��NT!VfY�Vfv�c�V�_RMPORQ�K c.�EY�ORQ9l

s

Page 11: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

��� � ���&25���������&$?.0/12#'�'��*. ) .�� �&%��(%��&�!%��9)\=Yt[8c9S�Y��NS![DY=h,�NTLv�c9T5�EQ�Q�K VfvNQ�SUQ�bNSUQ�TUQ�KHV£c�VfMPORQ�M^KNkNMPO=M^k���c9jÄYRSU_Hc9KNM^TUe c9TLctbNSUM^h�Q�V£c.�9Q�S�l�>LY/ �QV��NSUK%VfYÓVfvNQ�h�Y=YRSUkNM^K�c�VfM^YRK>Y9[*e>c9S��9Q�V!VfSfc9KNTfc9h�VfM^YRKNT��HW%T��NMPV£c.�Nj^Q�|De>c9S��9Q�V�h�j^Q�c9SUM^KN_�}ÇbNSUM^h�Q�T�l�\=M^KNh�QM^K VfvNQ�TUvNYRSdVdnXS��NK c9j^jbEYRb��Nj°c�VfM^YRKNT&MPO][DYRS9E�G;<JIDBDBDBKI�7 c9SUQÓh�YRKNTdV£c9KHVI�*c9K Q�h�YRTdW=TdVfQ�e c9j^j^Y=h�c�VfM^YRK^Q�9�IDBDBDBKI Q �#TSV�IonZ�9DI�Z�V�IDBDBDBKI�Z��#TSV `�M^T AD� ��� ��� 4 � MP[

nZ�9 � M V Q�9�I |�o9cH}MPO Z[O>G MPO g V QSO [DYRS�c9j^j!EHG <JIDBDBDBKI�7 : <JB |�o �4}

��vNQ�M^KNQ,+-��c9j^MPVXW TUM^_RKØM^K2|�o9cH}�h�YRSUSUQ�TUbEYRKNkNT�VfY%VfvNQ�h�YRKHORQ�KHVfM^YRK�c9jO=M^Q� M^K Q�h�YRKNYRe-M^h�Q,+-�NM^j^M��NSUM��Nec9K�c9jPW=TUM^T>Vfv�c�V�c9K Q���h�Q�TUT T��NbNbNjPW e>c�W �EQ.�:����V c9K Q���h�Q�TUT kNQ�e>c9KNk M^T%KNY9VI�Lh�YRe-b�c�VfM��Nj^Q;�MPVfvQ,+-�NM^j^M��NSUM��Ne l���vNM^T�KNY9VfM^YRK6�NVfT%�Q�j^jE[DYRS!VfvNQ�SUQ�TUY��NSUh�Q9l�iLY/�Q�ORQ�S,� �NM^YRe>c9TUT�VfSfc9KNTfc9h�VfM^YRKNT��EQ�V �Q�Q�KbNSUQ�k�c�VfYRSUTtc9KNkÜbNSUQ�W=T-SUQ,+-�NM^SUQ%VfvNQZQ,+-��c9j^MPVXW TUM^_RKÜc9TtM^e-bEYRTUQ�k M^KA|�o �4} �ÇTUM^KNh�QZM^K Vfv�c�Vth�c9TUQ.��c9KQ���h�Q�TUT�T��NbNbNjPW h�YRKNTdVfMPV���VfQ�T�c9K M^K�[DQ�c9TUM��NM^j^MPVXWRl � T�c9SU_��NQ�k M^K e-YRSUQ�kNQ�V£c9M^j�M^KØg]M^h£vNKNQ�Szc9KNk$1*Q�VfvNM^_|�~9qRqRmH} ��MPO Z[O u MPO g V(QSO�M^e-bNj^M^Q�T�Vfv�c�V%Q�c9h£v YRSU_Hc9KNM^TUe E&�Y��Nj^k j^YRTUQ e-YRSUQ Y/�K �NM^YRe>c9TUTtVfv�c9KVfvNQ�M^S�bNSUQ�k�c�VfYRSUT�c9h�V���c9j^jPWth�YRKNT��Ne-Q9l ��vNM^T!M^T!h�j^Q�c9SUjPW>c�kNM^TUQ,+-�NM^j^M��NSUM��Ne [DQ�c�V��NSUQ.�NTUM^KNh�QzYRSU_Hc9KNM^TUe E�Y��Nj^kZh�Q�SdV£c9M^KNjPW3�EQzQ�c9_RQ�S�VfYÓSUQ�h�j°c9M^e VfvNQzQ���h�Q�TUT�T��NbNbNjPW%Y9[�MPVfT!Y/�K��NM^YRe>c9TUT�l���vNM^T!Y��NTUQ�SdO9c�VfM^YRKvNM^_RvNj^M^_RvHVfTÓVfvNQ bNSUM^KNh�M^b�c9j�kNM*)0Q�SUQ�KNh�Q4�EQ�V �Q�Q�K SUQ�TUY��NSUh�Q h�YRKNTdVfSfc9M^KHVfT-M^K Q�h�YRKNYRe-M^h�e-Y=kNQ�j^T-c9KNk|�o �4}�l �XK c9K2Q,+-�NM^j^M��NSUM��Ne Y9[zc h�YRe-bEQ�VfMPVfMPORQZQ�h�YRKNYRe�W2c e>c9S��9Q�V-_RY=Y=k2M^T�M^K2Q���h�Q�TUT%T��NbNbNjPWÜMP[c9KNk YRKNjPW MP[aMPVfTtbNSUM^h�Q�M^T(7�Q�SUYNl >LYÙc9_RQ�KHV>M^TtM^KHVfQ�SUQ�TdVfQ�k M^K2h�j°c9M^e-M^KN_ VfvNQ Q���h�Q�TUT%T��NbNbNjPWÜTUM^KNh�QQ�ORQ�SdW<�EY=k�W v�c9TÓc9j^SUQ�c9k�W h�YRe-Q-[DYRS2!c9SUk �MPVfvÙvNM^T�YRS�vNQ�S�Tfc�VfM°c�VfM^YRK kNQ�e>c9KNkÄl iLQ�KNh�Q%Q�h�YRKNYRe-M^h_RY=Y=kNT�M^K%|DQ,+-�NM^j^M��NSUM��Ne%}EQ���h�Q�TUTÆT��NbNbNjPW�c9SUQÇ[DSUQ�Q�_RY=Y=kNT,�9c9KNk�VfvNQ�Q���h�Q�TUTÆT��NbNbNjPW�O9c9KNM^TUvNQ�T �HW�O=M^SdV��NQY9[�VfvNQZc9TUT��Ne-b�VfM^YRK Y9[�[DSUQ�Q%kNM^TUbEYRTfc9j�l ��Q�V �NM^YRe>c9TUT�Y9[�bNSUQ�W TUbEQ�h�M^Q�T�c9j*!c�W=T �v-�NSdVfT -VfvNQ%bNSUQ�Wc9KNkØvNQ�KNh�Q�h�c9KNKNY9V��EQ�c>[DSUQ�Q�_RY=Y=k M^K VfvNQÓTUQ�KNTUQ�Y9[ÇQ�h�YRKNYRe-M^h�VfvNQ�YRSdWRl�>LQ�MPVfvNQ�SzM^TL[DSUQ�QÓkNM^TUbEYRTfc9jY9[Q���h�Q�TUTaT��NbNbNj^M^Q�T�Y9[bNSUQ�W��NM^YRe>c9TUT�c�TUQ�KNTUM��Nj^Q�h�YRKNh�Q�b�VLM^K�Q�h�YRTdW=TdVfQ�e$c9K�c9jPW=TUM^T�l

JLKNj^M��9QÜ|�o �4} ��|�o9cH}-M^T>ORQ�SdW e0�Nh£v�M^K VfvNQØTUbNM^SUMPV%Y9[�Q�h�YRKNYRe-M^h SUQ�TUY��NSUh�Q h�YRKNTdVfSfc9M^KHVfT�c9KNkVfvNQ-SUQ�TUY��NSUh�Q>h�c9KÙSUM^_RvHVfjPW#�EQ-h�c9j^j^Q�kÙc.���NKNk�c9KHV�M^K h�c9TUQ-Y9[ nZ�9 u M V Q�9�l ��Q�V'�Q(�M^j^j]TUvNY/ Vfv�c�V��9CG m M^TÇYRKNjPW�T�� �-h�M^Q�KHV�����V�KNY9V�KNQ�h�Q�TUTfc9SdWt[DYRS]VfvNM^T�M^KNQ,+-��c9j^MPVXW�VfY�vNYRj^k-M^K-Q,+-�NM^j^M��NSUM��Ne l*iac�O=M^KN_Sfc�VfM^YRK�c9j^M�7�Q�ktVfvNQzQ,+-��c9j^MPVXW-TUM^_RKNT�M^K |�o �4}ÇMPV�TUvNY��Nj^k��EQ�c9kNkNQ�k%Vfv�c�V!TUQ�h,�NSUM^KN_ÓVfvNQ�TUQzQ,+-��c9j^MPVXW-TUM^_RKNT�M^j^jÄV��NSUK Y���VLVfY6�EQ�c-KNYRK=n�VfSUMPO=M°c9jÄM^TUT��NQ�M^K Q�TdV£c.�Nj^M^TUvNM^KN_-c9K Q,+-�NM^j^M��NSUM��Ne l=��vNQ�kNM��-h,�NjPVfM^Q�T�TdVfQ�e[DSUYRe VfvNQ M^e-bNj^M^h�c�VfM^YRKNTÓY9[�bNSUYRbEYRTUMPVfM^YRKÕ� Vfv�c�V6�MPVfv kNQ�e>c9KNk bNSUM^h�Q�T%c9bNbNSUYHc9h£vNM^KN_ 7�Q�SUY ��KNMPVfQ�Tfc�VfM°c�VfM^YRK%kNQ�e>c9KNkNT �c9SUQ�c�VUV£c9M^KNQ�kZ[DYRS�c9j^jÄTUbEQ�h�M^Q�T � �NM^YRe>c9TUT�l

�*Y-e>c.�9QzVfvNM^T�bEYRM^KHV�SUM^_RYRSUY��NTUjPW>h�YRKNTUM^kNQ�S�VfvNQ�[DYRj^j^Y/�M^KN_

����� #��/#�� �G#������! �" ( #&%�#'�"($#&% 8 �[� ��1�5 9��� 1 nZ�9 u m � ��� u m � MPO u m ��1 � ��O u m A$�[�E9G <JIDBDBDBKI�7 ��1 � � � �h5��h> � �r��4&4 � ����> �0� 1 ��A > � ��1*�D�M�h> �0� 1*� ^Q��9 IDBDBDBKI Q���#TSV I�Z�V IDBDBDBKI�Z�� ` ��1 � � ��� � � �^ ��9DIDBDBDBKI ���#TSV�` � �{�D� � � > � � � 1*�h> � > � > � �R�7@ �[� >/< � � 1 � � � �h5��h> � � �(' � � 4 ���K��� ���*) � � A{

Page 12: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

- � 6 ^Q��OUTSV I�Z�O `&� � 4 �� � -���6 A$�[� ��4&4SEHG <JIDBDBDBKI�7 �- �� 6*-��o�6 ��1 � -�� � 6 @ � 4 � ������ ���"!$#&%�#'�"(��O+ -/8 � � 4 � ��� ��A ���J� �h> � 1 � � ��A �(' � � 4 ���K��� ��� )=6� � > nZ�9 u m � ��� u m � MPO u m ��1 � ��O u m A$�[� E�G><JIDBDBDBKI�7 ��� 9��� 1 � �7@ �[� >/< � � 1 � � � �h5��h> � ��(' � � 4 ���K��� ���*) �M��� � 1 � > ���J� �h> � � 1 9�� 1 ��� ��4 �1]SUYRbEYRTUMPVfM^YRK ~ M^TÓQ�c9TUM^jPW bNSUY�ORQ�k �MPVfvÙVfvNQZvNQ�j^b Y9[%��_��NSUQ ~ Vfv�c�VÓM^j^j��NTdVfSfc�VfQ�T�O9c9SUM^Y��NT�TUh�Q�K�c9SUM^YRT[DYRS97rG��ZM^K#�vNM^h£v c%TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e kNY=Q�T�KNY9V�Q���M^TdV�l ��YRKNTUM^kNQ�S���SUTdV�VfvNQ�kNQ�e>c9KNk c9KNkT��NbNbNjPWth,�NSdORQ�T!M^KtVfvNQab�c9KNQ�j^T ��n ���AY9[@��_��NSUQz~zVfv�c�V!c9SUQLkNSfcI�K%c9T�TUYRj^M^k-j^M^KNQ�T�l ��j^Q�c9SUjPW��HVfvNQLbNSUM^h�Q�T^.�&'9 I�&'V I�&';�9 `�c9KNk ^.�&%9 I�&%V I�&%;�9 `zkNQ�VfQ�SUe-M^KNQtcÙ|F�NKNM�+-�NQ�}zQ,+-�NM^j^M��NSUM��Ne MP[�VfvNQtSUQ�TUY��NSUh�Q-Q�KNkNY/�e-Q�KHVM^TqnZ '9 c9KNk nZ %9 �]SUQ�TUbEQ�h�VfMPORQ�jPWRl ��vNQZQ,+-�NM^j^M��NSUM��Ne �MPVfv T��NbEQ�SUTUh�SUM^b�V� |DQ,+-�NM^j^M��NSUM��Ne� �][DYRS�TUvNYRSdV�}kNM*)0Q�SUT�[DSUYRe Q,+-�NM^j^M��NSUM��Ne b M^KØVfv�c�V�VfvNQ-SUQ�TUY��NSUh�Q-M^T�c.���NKNk�c9KHV�M^K Q,+-�NM^j^M��NSUM��Ne b ����V�TUh�c9SUh�Q-M^K �l � \<�NbNbEYRTUQ�KNY/ VfvNQ�_RSfc9bNv Y9[ÆVfvNQÓc9_R_RSUQ�_Hc�VfQ�T��NbNbNjPW�[F�NKNh�VfM^YRK M V�� V ^.��9�`�M^TLKNY9Va_RMPORQ�K#�HW�VfvNQTUYRj^M^k%j^M^KNQLM^KZb�c9KNQ�j � ��Y9[ ��_��NSUQ�~'����V�Sfc�VfvNQ�S��HW>VfvNQzk�c9TUvNQ�k j^M^KNQ9l ��vNQ�K c9KZQ,+-�NM^j^M��NSUM��Ne [8c9M^j^T�VfYQ���M^TdVLM^K�h�c9TUQ�Y9[Q�MPVfvNQ�S�SUQ�TUY��NSUh�Q�Q�KNkNY/�e-Q�KHVI�XnZ '9 YRSRnZ %9 �NTUM^KNh�Q�[DYRS �FG� SI b

M V�� V ^.� �9 ` u M ;�� V ^.�6V ` [DYRS�c9j^j �6V � m B��vNQ�SUQ�c9TUYRK�[DYRS�Vfv�c�V � TdVfS��Nh�V��NSfc9j � Q���h�Q�TUTLT��NbNbNjPWZM^T!VfvNQ!�EY��NKNkNQ�kNKNQ�TUT�|DYRS�Tfc�VfM°c�VfM^YRK4}ÇY9[*kNQ�e>c9KNk� V ^.�6V�`Æ[DYRS�c9j^j:�6V 5 l m I � ; p�l M^_��NSUQa~�M^j^j��NTdVfSfc�VfQ�T�c9KNY9VfvNQ�SÇ[8c9M^j��NSUQ�Y9[�c9K>Q,+-�NM^j^M��NSUM��Ne VfY�Q���M^TdV�l � Tc�bEYRM^KHV�Y9[ÆkNQ�b�c9SdV��NSUQ�h�YRKNTUM^kNQ�SLc9_Hc9M^K%VfvNQ�TUYRj^M^kNjPW>kNSfcI�K j^M^KNQ�T�c9KNk�VfvNQ�bNSUM^h�Q�T ^.� %9 I� %V I� %;�9 `�l ?ÙQ��KNY/ Vfv�c�VzVfvNM^TzM^T�c9K Q,+-�NM^j^M��NSUM��Ne TUh�Q�K�c9SUM^YNl0"A��V�MP[]VfvNQtc9_R_RSUQ�_Hc�VfQÓT��NbNbNjPW [F�NKNh�VfM^YRK�M ;�� ; ^.�6V `M^K b�c9KNQ�j ��� |DTUYRj^M^k�j^M^KNQ�}�M^T�SUQ�bNj°c9h�Q�k4�HW�VfvNQ�k�c9TUvNQ�k j^M^KNQ!�Q�Q�KNk#�Nb;�MPVfv c9K Q���h�Q�TUTzT��NbNbNjPW�YRKVfvNQ�e>c9S��9Q�V�[DYRS%�NM^YRe>c9TUT�Y9[TUbEQ�h�M^Q�Tz~=l � _Hc9M^K@�Nc9K Q,+-�NM^j^M��NSUM��Ne h�c9KNKNY9V:�EQ�Q�TdV£c.�Nj^M^TUvNQ�kÄl

� TLkNSfcI�K M^K���_��NSUQ�~�MPV�M^T!VfvNQ�bNSUQ�k�c�VfM^YRK�SUM^T��%h�YRKNTdVfSfc9M^KHVÓ|8mH}�Vfv�c�VLM^T�SUQ�TUbEYRKNTUM��Nj^Qz[DYRS�VfvNQ�EY��NKNkNT�YRK kNQ�e>c9KNkÄl0"A��V�M^KØ_RQ�KNQ�Sfc9j��ÄkNQ�e>c9KNkØTfc�VfM°c�VfM^YRKÜ|8c�V!7�Q�SUY�bNSUM^h�Q�}aM^TzY9[�h�Y��NSUTUQtM^e-bNj^M^Q�k�HWÜe>c9KHW [F�NKNh�VfM^YRK�c9j�[DYRSUe-TNc O Q�ORQ�K MP[�|8mH}&�Y��Nj^k2KNY9V%c9bNbNjPWRl � YRSUQ�Y�ORQ�S,��kNQ�e>c9KNk2Tfc�VfM°c�VfM^YRKe0�NTdV��EQÓh�YRKNTUM^kNQ�SUQ�kÙc%SUQ�c9j^M^TdVfM^h�[DQ�c�V��NSUQ�M^K Q�h�YRTdW=TdVfQ�e c9K�c9jPW=TUM^T,�ÄTUM^KNh�Qtc9j^jYRSU_Hc9KNM^TUe-T � h�c9b�c9h�MPVXWY9[�V£c.��M^KN_ÓM^K�c9KNk�kNM^_RQ�TdV![DY=Y=k%M^T!j^M^e-MPVfQ�k-M^K%VfvNQ�TUvNYRSdVdnXS��NKZbEQ�SUM^Y=k | �vNM^h£v c9bNbNj^M^Q�T�VfY�v-�Ne>c9KNT�c9T�Q�j^jÂ}�l!��vNQ�SUQ�[DYRSUQtkNQ�e>c9KNkØTfc�VfM°c�VfM^YRK h�YRe0�NM^KNQ�k#�MPVfv VfvNQ�Q,+-��c9j^MPVXW |��³}2|�o �4}LbEYRTUQ�T�c%bEQ�SUTUM^TdVfQ�KHVQ���M^TdVfQ�KNh�Q�bNSUY��Nj^Q�e l�gÆORQ�K MP[Æc9K Q,+-�NM^j^M��NSUM��Ne h�c9K4�EQ�TUvNY/�K VfY-Q���M^TdVaM^K ct_RMPORQ�K bEQ�SUM^Y=k@��MPVLe>c�WKNY9V�Q���M^TdVLM^K�TUYRe-Qz[F��V��NSUQ�bEQ�SUM^Y=k�kNQ�bEQ�KNkNM^KN_tYRK vNY/�TUbEQ�h�M^Q�T�bEYRb��Nj°c�VfM^YRKNT!_RSUY/�YRS�TUvNSUM^K��4l

��vNQ�TUQth�YRKNTUM^kNQ�Sfc�VfM^YRKNTaT��N_R_RQ�TdV�Vfv�c�V�M^K YRSUkNQ�SaVfYZbNSUY�O=M^kNQ�c%_RQ�KNQ�Sfc9jbNSUY=Y9[ÇY9[ÇQ,+-�NM^j^M��NSUM��Ne�MPVfvNY���V�c.��c9KNkNYRKNM^KN_ VfvNQ%h�YRKNTdVfSfc9M^KHVfTZ|8mH}�Q�KHVfM^SUQ�jPW YRKNQ%KNQ�Q�kNTÓV �YØM^KN_RSUQ�kNM^Q�KHVfT�l M^SUTdVI�M^KÙVfvNQ

� É�©�µI­�¬�©�´ µ�¯�«�¶�¶8´ µIÈ�¬�·�«£¬Æ´ µ�Ö�È�ºI¨�©5E�¿0©�«�¶�¶8´ È�µI©Uª����F ~X[ �fÊR¾Iº�¬]«�² ²�¯I¨�´³¸¹©U¶ N����F f ���� f ���! F P�¿�´ ¬�·"���F$#&% Y�f0[ � '¸¹­�µ�¶D¬�´ ¬�º�¬�©Ç«�µa©UÑ�ºI´ ² ´ ¾I¨�´ ºI½zÊ�¬�­�­�Ê�©U«�¸�·a­�»�¿�·I´³¸�·z©¹Ë�·I´ ¾I´ ¬�´ µIÈ�¬�·I©Ç¶�«�½!©Æ©UÑ�ºI´ ² ´ ¾I¨�´ ºI½ «�² ² ­�¸d«£¬�´ ­�µ�À

��q

Page 13: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

M^_��NSUQ�~=w ��vNQ�Q���M^TdVfQ�KNh�Q�bNSUY��Nj^Q�e

c.�NTUQ�KNh�Q Y9[-|8mH}ÓkNQ�e>c9KNk2Tfc�VfM°c�VfM^YRK2c�V-bNSUM^h�Q�TtVfQ�KNkNM^KN_ VfY 7�Q�SUYÙe0�NTdV6�EQ S��Nj^Q�k2Y���V��I��c9KNk TUQ�h�nYRKNk@��VfvNY��N_Rv bEYRTUMPVfMPORQ ��OSUQ�KNkNQ�SakNQ�e>c9KNkNT5�EY��NKNkNQ�kØc�VLj^Y/�bNSUM^h�Q�T,��VfvNQ�b�c9Sfc9e-Q�VfQ�SUT ��O*e0�NTdV �EQkNQ�VfQ�SUe-M^KNQ�kÓQ�KNkNYR_RQ�KNY��NTUjPW�VfYzc9j^j^Y/ [DYRS*e-YRSUQXx�Q���M��NM^j^MPVXW�Y9[4kNQ�e>c9KNkNTÆc9KNkÓT��NbNbNj^M^Q�T]c�Vj^Y/ÜbNSUM^h�Q�T�l

�*Y�e>c.�9QzbNSUYR_RSUQ�TUT,���Q!��c9TUQ�Y��NS!T����NTUQ,+-�NQ�KHVzc9K�c9jPW=TUM^T�YRKZKNQ�V%�NM^YRe>c9TUT�[F�NKNh�VfM^YRKNT�W=M^Q�j^kNM^KN_kNQ�e>c9KNk c9KNk T��NbNbNjPW%[F�NKNh�VfM^YRKNT%�MPVfvZVfvNQ�[DYRj^j^Y/�M^KN_�bNSUYRbEQ�SdVfM^Q�T�w

� !$! ���`�V%�#'�"(;) % � � 1 � > � � 5��� OUTSV ��1 � �� O >&@ �F��� �N��1 � ��1 � ���2�3�"4�5 A � 1 �h> �0� 1 ��A �[�09 ��1 � ���E � 1X>&@ � � � � � 1 � � ��A � � 1*�h> � � � 1�> -��h6 �� N µI­�µ�®Â¶�«£¬�´³«£¬�´ ­�µz«�¶�¶8ºI½!¯�¬�´ ­�µz­�»N¬�·I´³¶Ä¬D±�¯9©Ç´³¶�µI©d©Uª�©Uªz´ µ�©¹Ë�´³¶D¬�©dµ�¸¹©]¯I¨�­�­�»P¶�´ µ�«�² ²�æ*©d¾I¨�©dº�®^¬D±�¯9©]È�©dµI©d¨�«�²H©UÑ�ºI´ ®

² ´ ¾I¨�´ ºI½2½!­�ª�©d²³¶ DPæ*©d¾I¨�©dº0E�G G,KXÀ

�R�

Page 14: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

- � 6 �� OUTSV w m ��1 ��� � � ��� �� 9 �� OUTSV ^.�SOUTSV `#G�� A$�[� EHG <JIDBDBDBKI�7 �- �� 6�� @ ����� � ���SOUTSV � m �����7@ >&@!��> �� O ^.�SOUTSV ` / m A$�[� ��4&4:�SOUTSV ���SOUTSV �� TUT��Ne-b�VfM^YRK �%M^T�c e-M^j^k SUQ�TdVfSUM^h�VfM^YRKÙYRKNjPWRl ��VÓM^T�Tfc�VfM^T2��Q�k@�ÆQ9l _Nl*� �HWÙKNQ�V �NM^YRe>c9TUT�[F�NKNh�VfM^YRKNT�Y9[��Y����=n¹`aY��N_Rj°c9T�VXW=bEQ9l ��vNQ TUM^_RKNT-Y9[aVfvNQ b�c9SdVfM°c9j^T�Y9[aVfvNQ�[F�NKNh�VfM^YRKNT �� OUTSV c9KNk �� O kNQ�bEQ�KNk YRKVfvNQ�TUM^_RKNTLY9[VfvNQ�M^KNh�YRe-Q�c9KNk T����NTdVfMPV���VfM^YRK Q�)0Q�h�V�l�\<�NbNbEYRTUQ�VfvNQ�M^KNh�YRe-Q�Q�)0Q�h�VzM^T�bEYRTUMPVfMPORQ!�MPVfvSUQ�TUbEQ�h�V!VfY QSOUTSV�c9KNk%KNQ�_Hc�VfMPORQ:�MPVfv%SUQ�TUbEQ�h�V!VfY Z[O]| �vNM^h£v6�Y��Nj^k��EQah�YRKNTUM^kNQ�SUQ�k%VfvNQLVXW=bNM^h�c9jEh�c9TUQM^K�h�YRKNT��Ne-Q�S*VfvNQ�YRSdWN}�l ��V*[DYRj^j^Y/�T�VfvNQ�K �NK�c9e0�NM^_��NY��NTUjPWzVfv�c�V �� OUTSV w m l �� O M^T*TdVfM^j^jHM^KNkNQ�VfQ�SUe-M^K�c�VfQM^KZTUM^_RK��EQ�h�c.�NTUQ�VfvNQ�KNQ�_Hc�VfMPORQzM^KNh�YRe-QaQ�)0Q�h�VLM^T!c9h�h�YRe-b�c9KNM^Q�k��HWZcÓbEYRTUMPVfMPORQzT����NTdVfMPV���VfM^YRK%Q�)0Q�h�V�l�YRj^j^Y/�M^KN_�c9_Hc9M^K%VfvNQ�bNSUQ�O9c9M^j^M^KN_ÓbNSUYRbEYRTUMPVfM^YRK%M^K�h�YRKNT��Ne-Q�S�VfvNQ�YRSdW%Vfv�c�V�VfvNQ�j°c.�EYRS!T��NbNbNjPWZh,�NSdORQM^T=�Nb !c9SUkZTUj^YRbNM^KN_'�Q�c9TUT��Ne-QavNQ�SUQaVfv�c�V�VfvNQzKNQ�_Hc�VfMPORQaM^KNh�YRe-Q�Q�)0Q�h�V�kNY=Q�T�KNY9V!Y�ORQ�SUh�YRe-bEQ�KNTfc�VfQVfvNQ�bEYRTUMPVfMPORQ�T����NTdVfMPV���VfM^YRK�Q�)0Q�h�V�l�iLQ�KNh�Q �� O / m l

1]SUM^YRS�VfY�h£vNQ�h��M^KN_ �vNQ�VfvNQ�S!VfvNQaQ���M^TdVfQ�KNh�Q�bNSUY��Nj^Q�e Y9[�bNSUYRbEYRTUMPVfM^YRK%~�h�c9K��EQaY�ORQ�SUh�YRe-Q��HW� TUT��Ne-b�VfM^YRKØ��c9KNkZVfvNQzb�c9Sfc9e-Q�VfQ�SUT ��O�MPV�M^T�KNQ�h�Q�TUTfc9SdWZVfY�e-Y=kNMP[ÂWtVfvNQ�Q,+-�NM^j^M��NSUM��Ne kNQ���KNMPVfM^YRKZc9T[DYRj^j^Y/�T�w

����� #��/#�� �G#���� �! �" ( #&%�#'�"( # #&% 8 �[� ��1�5 9��� 1dnZ�9 u m � ��� u m ��1 � MPO u m A$�[� E G<JIDBDBDBKI�7 ��1 � � � �h5��h> � � ��4&4 � ����> �0� 1 ��A > � ��1*�D�M�h> �0� 1*�N^Q��9 IDBDBDBKI Q���#TSV I�Z�V IDBDBDB�I�Z�� ` � � ��� � � �N^ ��9DIDBDBDBKI���#TSV�` ��1 � �!� � �� � > ��� � ^ �DV�IDBDBDBKI � �C` � � �D� � � > � � � 1*�h> � > � > � � �7@ �[� >/< � � 1 � � � �h5��h> � � �(' � � 4 ���K��� ���) ) � � A- � 6 ^Q��OUTSV I�Z�O `&� � 4 �� � -���6 A$�[� ��4&4SEHG <JIDBDBDBKI�7 �- �� 6*-��o�6 ��1 � -�� � 6 @ � 4 � ������ ���"!$#&%�#'�"(��O+ -� �J� �h> � 1 � � ��1 � � ��� � ��� > � � � ��A �(' � � 4 ���K��� ���*) )=6� � > nZ�9 u m � �DV u m � ��� u m ��1 � MPO u m A$�[� E G <JIDBDBDBKI�7 ��� 9��� 1]��1 � ���2�3� � � � >&@!��> �������O�"> �0� 1�� @ � 4 � � �- � 6�� @ ����� ���J� �h>� ��1 � � � �h5��h> � � �(' � � 4 ���K��� ���*) ) �- �� 6 )1 �(' � � 4 ���K��� ��� >&@ � ��� � � � � � � � � � � � 1 � ��1�> � A ��1 �:� 1�4�5 � A M V w nZ�9 � � V ^ �DV�` �- ��� 6 ) A >&@ �&��� � � � � � �s� �9� � � 1 � ��1�> � 1 ��1 �(' � � 4 ���K��� ��� >&@ � 1 ��4&4*��� � � � � �&� ��� � � � 1 � ��1�> � 1:>&@ � � � 1*� �

>&@!��> >&@ � � ��� � �R�� �h> �[� ^ ��9 G m I �1V9G m IDBDBDBKI ���#TSV&G m `N��4 � 1 9��5� >&@D>&@ � � � �h> �!� � �� � > ��� �������O g V#G��� O�� ��O MPOMPO g V � OUTSV ^ ��Oa`�� A$�[� EHG <JIDBDBDBKI�7 : < � � 1*�h> � > � > � ��1 �(' � � 4 ���K��� ��� �

- �� 6 ) A >&@ �F��� � � � � � �s� � 1 � >f� � � 1 � ��1�> � 1 ��1 �(' � � 4 ���K��� ��� ��4&4*��� � � � � �s� ��� �2��� � � �F� 1:>&@ � � � 1*� � >&@!��>��4&4 �(' � � 4 ���K��� ��� � ��� � � � � ��� � � � � > ��� ������� � ª�©dµI­�¬�©U¶Æ¬�·I©L´ µ�Ã�©d¨�¶8©�­�»Ä¬�·I©Lª�©d½�«�µ�ª�»¼ºIµ�¸X¬�´ ­�µ � � N�[(� !*� PXÀ�çI­�¨Ç½!­�¨�©�ª�©¹¬�«�´ ²³¶Ç¿0©�¨�©¹»¼©d¨]¬�­�¬�·I©L¯I¨�­�­�»�­�»¯I¨�­�¯9­�¶8´ ¬�´ ­�µ O!´ µL¬�·I© N ¯I¯9©dµ�ª�´ ËHÀ

�I~

Page 15: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

� T�VfvNQ�bNSUY=Y9[�Y9[�bNSUYRbEYRTUMPVfM^YRKØmZM^K VfvNQ � bNbEQ�KNkNM¼�ØTUvNY/�T�VfvNQtb�c9Sfc9e-Q�VfQ�SUT ��O�c9SUQtQ�KNkNYR_RQ�KNY��NTUjPWh£vNYRTUQ�K�M^K%T��Nh£v c'!c�W>Vfv�c�V!M^K6��_��NSUQ�~�VfvNQzbEYRM^KHVfT ) c9KNk_c h�YRM^KNh�M^kNQzc9KNk>VfvNQzj^M^KNQaTUQ�_Re-Q�KHV m ,�EQ�h�YRe-Q�T�Q,+-��c9jÇVfY m�� lZ`aSfcI�M^KN_ c9K c9bNbNSUYRbNSUM°c�VfQ�jPWØe-Y=kNM*��Q�k kNM°c9_RSfc9e;��YRKNQ-h�c9KÙQ�c9TUM^jPWØh£vNQ�h�Vfv�c�V(�NKNkNQ�S�VfvNQ�TUQ�h�YRKNkNMPVfM^YRKNT�|8c9KNk �MPVfv � TUT��Ne-b�VfM^YRK��I}�VfvNQZQ���M^TdVfQ�KNh�Q Y9[zc9KÜQ,+-�NM^j^M��NSUM��Ne M^TTUQ�h,�NSUQ�kÄl ��V]V��NSUKNT]Y���V]Vfv�c�V]kNQ�bEQ�KNkNM^KN_�YRKÓVfvNQ�c.���NKNk�c9KNh�Q�YRSÆTUh�c9SUh�MPVXWÓY9[4VfvNQ�SUQ�TUY��NSUh�Q�VfvNQ�Q�KHVfM^SUQQ�h�YRTdW=TdVfQ�e M^T�Q�MPVfvNQ�S�c.���NKNk�c9KHV�|DbNSUYRbEYRTUMPVfM^YRK-m�M^M^MÂ}*YRS�TUh�c9SUh�Q�|DbNSUYRbEYRTUMPVfM^YRK-m�MPON}�l]\=h�c9SUh�MPVXW-Y9[0VfvNQSUQ�TUY��NSUh�Q�c9KNk%VfvNQ�TUbEQ�h�M^Q�T�M^T!SUQ�x�Q�h�VfQ�k M^KZc9j^j0SUQ�j°c�VfMPORQaQ,+-�NM^j^M��NSUM��Ne bNSUM^h�Q�T%�EQ�M^KN_ÓTdVfSUM^h�VfjPW>bEYRTUMPVfMPORQ|DbNSUYRbEYRTUMPVfM^YRK m%MPON}�l{yzK VfvNQÓY9VfvNQ�Sav�c9KNk@��c.���NKNk�c9KNh�QÓh�c9K$�EQ�c9TUTUY=h�M°c�VfQ�k4�MPVfvØc9j^j�bNSUM^h�Q�T��EQ�M^KN_7�Q�SUY |DbNSUYRbEYRTUMPVfM^YRK�mtM^M^MÂ}�l ��VLM^T�M^e-bEYRSdV£c9KHV!VfYtKNY9VfQ.�4vNY/�Q�ORQ�S,�4Vfv�c�Vac9S��NMPVfSfc9SdW%bNSUM^h�Q�T-�SO750p m I ��O g V p[DYRSFE#G m ID<JIDBDBDB�I�7L:=<Óc9SUQ�c9j^TUY-h�YRe-b�c�VfM��Nj^Q��MPVfv c9K Q,+-�NM^j^M��NSUM��Ne Y9[Çc9K c.���NKNk�c9KHVzQ�h�YRTdW=TdVfQ�e l\=Ytj^YRKN_-c9T�VfvNQ�SUQ�TUY��NSUh�Q�M^T�c.���NKNk�c9KHVI�4bNSUM^h�Q�T�kNY-KNY9V�_��NM^kNQzVfvNQ�Q�h�YRTdW=TdVfQ�e$c9j^j^Y=h�c�VfM^YRKÄl

����� � 2X)��9"5�!" �*%��#. '��*" �*%(/1',2 '��&25���������&$ .0/12#'�'��*. ) .�� �&%��(%��&�!%("�XK VfvNM^T�T����NTUQ�h�VfM^YRK;�Q�Q���bNj^YRSUQ�vNY/ Q�h�YRTdW=TdVfQ�e$Q,+-�NM^j^M��NSUM°cÓc9SUQ�c )0Q�h�VfQ�k4�HW�h£v�c9KN_RQ�TaM^K Q�KHO=M^SUYRK=ne-Q�KHV£c9j0b�c9Sfc9e-Q�VfQ�SUT�l �*Y �EQ�h�YRKNh�SUQ�VfQ.���Q�SUQ�TdVfSUM^h�V�Y��NS�c�VUVfQ�KHVfM^YRK>VfYtc9KZQ�h�YRTdW=TdVfQ�e M^K6�vNM^h£vZVfvNQSUQ�TUY��NSUh�Q�M^T�TUh�c9SUh�Q.�Ec9KNk��Q�T��NbNbEYRTUQ�Vfv�c�V � TUT��Ne-b�VfM^YRK ����M�l Q9l

QSOUTSV#G �� OUTSVFe �SOUTSVT h c9KNk Z[O1G �� Ofe �SOUTSVT � 9 h EHG�<JIDBDBDB�I�7�I |8rH}

M^T�Tfc�VfM^T2��Q�kÄl

��V�M^T!Q�c9TdW>VfY�TUQ�QzVfv�c�V!VfvNQzTdW=TdVfQ�e Y9[*Q,+-��c�VfM^YRKNT�|�o9cH}�c9KNkÙ|�o �4}Çh�c9K��EQzTUYRjPORQ�k�����VUVfYRe �NbÄwnZ�9 G+Q��9 kNQ�VfQ�SUe-M^KNQ�T����9 c9KNk Z�V �0Z�V G+Q�� V M^e-bNj^M^Q�T ���V c9KNk _RMPORQ�T��NT Z�; ��c9KNk ��K�c9j^jPW Z�; G+Q��; M^Tc�VUV£c9M^KNQ�kÙ[DYRS ��; G ���; l$��vNQZY��NTUQ�SdO9c�VfM^YRKÙVfv�c�V�VfvNQZQ,+-�NM^j^M��NSUM��Ne h�c9K �EQ%kNQ�VfQ�SUe-M^KNQ�k TdVfQ�b �M^TUQ[DSUYRe TUbEQ�h�M^Q�T m VfY�TUbEQ�h�M^Q�T 7 M^TÇh�j^Q�c9SUjPW�k��NQ�VfY�Y��NS�e-Y=kNQ�j^M^KN_aVfvNQLQ�h�YRTdW=TdVfQ�e c9T�c��NKNM^kNM^SUQ�h�VfM^YRK�c9j[DY=Y=k h£v�c9M^K �vNYRTUQØbNSUM^KNh�M^b�c9jac�VUVfSUM�����VfQ M^T%kNQ�bEQ�KNkNQ�KNh�Q Sfc�VfvNQ�S>Vfv�c9K M^KHVfQ�SUkNQ�bEQ�KNkNQ�KNh�Q9l � T�ch�YRKNTUQ,+-�NQ�KNh�Q.�HTUvNY=h��T�|DM�l Q9l*b�c9Sfc9e-Q�VfQ�S�h£v�c9KN_RQ�T£}�M^K�VfvNM^T*Q�h�YRTdW=TdVfQ�eÒM^KNk��Nh�Q�SUQ�bEQ�SUh,�NTUTUM^YRKNT �EY9VUVfYRe�Nb3����V�KNY9V]VfYRbtkNY/�KÄl �*Y�e>c.�9Q�VfvNM^TÆ[DQ�c�V��NSUQ�e-YRSUQ�bNSUQ�h�M^TUQLc9KNk�VfY�TUvNY/��=c�V]VfvNQ�Tfc9e-Q�VfM^e-Q.�9VfvNQSUM^h£vNKNQ�TUT�M^KØM^e-bNj^M^h�c�VfM^YRKNTLY9[�Y��NS�e-Y=kNQ�jY9[�TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne �Q-KNY/ bNSUY=h�Q�Q�k�MPVfv cZh�YRe-b�c9Sfc�VfMPORQ�TdV£c�VfM^htc9K�c9jPW=TUM^T�l0?�MPVfvNY���V�j^YRTUT�Y9[�_RQ�KNQ�Sfc9j^MPVXW4�QtTUM^e-bNj^MP[ÂW�VfvNQtQ���bEYRTUMPVfM^YRK�HWZTUQ�VUVfM^KN_ � � 7>G �tc9KNk vNQ�KNh�Q��Q�TdV£c9SdVLY���V%�MPVfv c9K�M^KNMPVfM°c9jETUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne� � Áµ�ºIµI´³ª�´ ¨�©U¸X¬�´ ­�µ�«�²=»¼­�­�ª�¸�·�«�´ µ�¶�¬�·I¨�©d©Ç¬D±�¯9©U¶*­�»0¶8¯9©U¸¹´ ©U¶*µI©d©Uªz¬�­L¾9©!ª�´³¶D¬�´ µIÈ�ºI´³¶8·I©UªHà�¬�·I©�¶8¯9©U¸¹´ ©U¶QY'D¼¾Iº�¬8¬�­�½5KXÊ

¬�·I©�¶8¯9©U¸¹´ ©U¶ C Dè¬�­�¯.K«�µ�ª�«�² ²N­�¬�·I©d¨Ç¶8¯9©U¸¹´ ©U¶´ µ�¾9©¹¬D¿0©d©dµ�À N ² ²4¶8¯9©U¸¹´ ©U¶f}�¾9©¹¬D¿0©d©dµÓ«�¨�©!¸¹² ©U«�¨�² ±�«�² ´ Ï�©�´ µ�¬�·I©�¶8©dµ�¶8©¬�·�«£¬0¬�·I©d±�¯I¨�©d±�­�µa¶8¯9©U¸¹´ ©U¶P} j �Æ«�µ�ª�«�¨�©*¯I¨�©d±�©Uª�ºI¯9­�µL¾�±�¶8¯9©U¸¹´ ©U¶1}GRN��ÀNÁµa¸d«�¶8©*­�» C ~���¶8¯9©U¸¹´ ©U¶�âÇ´³¶E¬�·I©­�µI² ±µI­�µ�®°¾9­�ºIµ�ªI«�¨�±!¶8¯9©U¸¹´ ©U¶0¾Iº�¬Ä´ ¬Ä´³¶Ä¸¹² ©U«�¨�² ±�¨�©d¯I¨�©U¶8©dµ�¬�«£¬�´ Ã�©�»¼­�¨Ä«�² ²R´ µ�¬�©d¨�½!©Uª�´³«£¬�©¶8¯9©U¸¹´ ©U¶E´ µ�»¼­�­�ªL¸�·�«�´ µ�¶E² ­�µIÈ�©d¨4¬�·�«�µC ~��IÀ

��m

Page 16: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

Vfv�c�V�M^T![F�Nj^jPW%h£v�c9Sfc9h�VfQ�SUM�7�Q�k;�HW%VfvNQ�Q,+-��c�VfM^YRKNT

nZ�9CG=M V(Q�9�I M V(Z�V#G=M ;�Q6V�I M ;�Z�; GAM���Q�;DIQSOUTSVXG �� OUTSV ^.�SOUTSV ` c9KNk Z[O6G �� O ^.�SOUTSV�` EHG <JI�@�I �*B |�pR}

?ÙQ-KNY/ M^KHVfSUY=k��Nh�Q-b�c9Sfc9e-Q�VfSUM^hth£v�c9KN_RQ�TZ|DTUvNY=h��T£} �ÆYRKNQ>c�VÓc�VfM^e-Q.��M^K VfvNQ-b�c9Sfc9e-Q�VfQ�SUT nZ�9I�HM V �M ;�c9KNkYM���c9KNk kNQ�VfQ�SUe-M^KNQÓVfvNQ�h£v�c9KN_RQ�T�M^KNk��Nh�Q�k M^KØVfvNQ�Q�KNkNYR_RQ�KNY��NT�O9c9SUM°c.�Nj^Q�T ��9/� �6V�� ��;/�6Q�9/�Q6V��1Q�;/�6Z�V �1Z�;I�6Z��I� b V�� b ;�c9KNk b ��l � TzTUvNY/�K M^K VfvNQ�c9bNbEQ�KNkNM¼� �0VfY9V£c9jkNM*)0Q�SUQ�KHVfM°c�VfM^YRK Y9[]VfvNQ�TUQ�VY9[*Q,+-��c�VfM^YRKNT�|�pR}]W=M^Q�j^kNT�VfvNQzSUQ�T��NjPVfT�T��Ne-e>c9SUM�7�Q�k>M^K%V£c.�Nj^Q � �vNQ�SUQ �v�c�VfT zc.�EY�ORQ�j^Q�VUVfQ�SUT!kNQ�KNY9VfQSUQ�j°c�VfMPORQ�h£v�c9KN_RQ�TÓ|DQ9l _Nl �Q G��JQ ��Q0}�l ��vNQ�TUM^_RKNT�M^K��NSfc9h�9Q�VfTaM^KNkNM^h�c�VfQaVfvNQ�TUbEQ�h�M°c9j�h�c9TUQ �� O G m l

���9 ��6V ���; �Q�9 �Z�V �Q6V �Z�; �Q�; �Z�� �b V �b ; �b ��nZ�9 u m : : : � � � � � � ���v^�� ` ���v^ m ` ��� ^ m `�M V u m � ���v^(:9`����v^ m ` : : ���v^�� `���v^ m ` ��� ^ m ` ���v^ m ` ���v^(:9`��� ^�� ` ��� ^ m `�M ; u m q � ���v^ m ` q q : : ���v^�� `���v^ m ` m ��� ^(:9`���v^�� `�M�� u m q q � q q q q : : q q ���v^(:9`

�c.�Nj^Q �£w���YRe-b�c9Sfc�VfMPORQ�TdV£c�VfM^h�T�Y9[*VfvNQ�TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM��Ne

�Q�c�O=M^KN_ Y���VÓTUYRe-Q-kNQ�V£c9M^j^T�c9KNk TUbEQ�h�M°c9j][DQ�c�V��NSUQ�T�Y9[!V£c.�Nj^Q �aVfvNQ>bNSUM^KNh�M^b�c9j]SUQ�T��NjPVfT�Y9[!VfvNQQ���Q�SUh�M^TUQ�M^K�h�YRe-b�c9Sfc�VfMPORQzTdV£c�VfM^h�TLc9SUQ9w

|DMÂ} ��[!VfvNQ>SUQ�TUY��NSUh�Q>Q�KNkNY/�e-Q�KHV�Y9[�VfvNQ>Q�h�YRTdW=TdVfQ�e |8c9j^M°c9TzVfvNQ � T��NbNbNjPW Y9[��NM^YRe>c9TUT�Y9[!TUbEQ�h�M^Q�Tq � }�M^KNh�SUQ�c9TUQ�T,�ÆVfvNQ�KÜc9j^jÇTUbEQ�h�M^Q�T � VfQ�SUe-T�Y9[�VfSfc9kNQ>M^e-bNSUY�ORQ � 9�c9KNkÜc9j^jÇe>c9S��9Q�V�VfSfc9KNTfc9h�VfM^YRKNTQ���b�c9KNkÄl

|DM^MÂ}���[*VfvNQ�bEYRb��Nj°c�VfM^YRK%Y9[TUbEQ�h�M^Q�TsEÇM^KNh�SUQ�c9TUQ�T,�NVfvNQ�K YRSU_Hc9KNM^TUeLE� [8c9h�Q�T6�YRSUTUQ VfQ�SUe-T>Y9[zVfSfc9kNQ.�%�vNM^j^Q�VfvNQ Y9VfvNQ�S>TUbEQ�h�M^Q�T � VfQ�SUe-T>Y9[�VfSfc9kNQ VfQ�KNk VfY �EQKNYRK=nXkNQ�VfQ�SUM^YRSfc�VfM^KN_ �

� SUQ�k��Nh�Q�TLMPVfT�e>c9S��9Q�V�VfSfc9KNTfc9h�VfM^YRKNT �

� SUQ�k��Nh�Q�T MPVfTZY.)0TUbNSUM^KN_��:�vNM^j^Q VfvNQ Y.)0TUbNSUM^KN_ÜY9[�VfvNQ Y9VfvNQ�S�TUbEQ�h�M^Q�T�VfQ�KNk�VfY �EQ KNYRK=nkNQ�h�SUQ�c9TUM^KN_Nl

|DM^M^MÂ} ��[�[DYRS E G @�I � TUbEQ�h�M^Q�T EzQ���bEQ�SUM^Q�KNh�Q�Ttc h£v�c9KN_RQZM^K MPVfT�bEYRb��Nj°c�VfM^YRK@�*TUbEQ�h�M^Q�T � w EzM^TÓKNY9Vc�Vac9j^j�c )0Q�h�VfQ�k4�HW�VfvNM^T�h£v�c9KN_RQ9w!MPVfT�VfQ�SUe-TLY9[VfSfc9kNQ.�4MPVfT�VfSfc9KNTfc9h�VfM^YRKNTLc9KNk MPVfT�KNQ�V �NM^YRe>c9TUTSUQ�e>c9M^K��NKNh£v�c9KN_RQ�kÄl

�FB�� ¾�¶8©d¨�Ã�©0¬�·�«£¬ ������ ~ E����� J=E� k�YÆ´ ½!¯I² ´ ©U¶�¬�·�«£¬0¶8¯9©U¸¹´ ©U¶S}=´³¶4«�¾I² ©Ä¬�­Ç¯IºI¨�¸�·�«�¶8©Ä½!­�¨�©Ä¾I´ ­�½�«�¶�¶�­�»R¯I¨�©d±�¶8¯9©U¸¹´ ©U¶} j ��À��y

Page 17: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

��vNQ!j°c9TdVY��NTUQ�SdO9c�VfM^YRK�|DM^M^MÂ}0M^TM^KHVfSUM^_��NM^KN_��IMP[�KNY9Vh�Y��NKHVfQ�SUM^KHV��NMPVfMPORQ.������VÆYRKNjPW�VfYLVfvNQ!Q��=VfQ�KHVÆVfv�c�V �Qj^Q�V]Y��NSÆM^KHV��NMPVfM^YRK�SUQ�jPW�YRKtb�c9SdVfM°c9j=Q,+-�NM^j^M��NSUM��NeÒc9SU_��Ne-Q�KHVfT�l��*Y�TUQ�Q�Vfv�c�VI�Rh�YRKNTUM^kNQ�SÇc9K�Q,+-�NM^j^M��NSUM��NeY9[*VfvNQ�e>c9S��9Q�V�[DYRS%�NM^YRe>c9TUT!Y9[TUbEQ�h�M^Q�Tz~Ó_RMPORQ�K;�HW

M�� �� ;9e ��;T I � �g h G=M ; �� ;9e ��;g I �1VT h I |8sH}

�vNQ�SUQ �1V � ��;Æc9KNk�� �Æc9SUQ�c9TUT��Ne-Q�k�VfY �EQÇ_RQ�KNQ�Sfc9j�Q,+-�NM^j^M��NSUM��NeAbNSUM^h�Q�T�lÆ\<�NbNbEYRTUQ�KNY/��M��M^T�TUj^M^_RvHVfjPWM^KNh�SUQ�c9TUQ�k>VfY M � � u M��A�vNM^j^Q�Q�ORQ�SdW�VfvNM^KN_ÓQ�j^TUQaM^T=�9Q�b�V!h�YRKNTdV£c9KHV!Q���h�Q�b�V!VfvNQabNSUM^h�Q ��;�l ��j^Q�c9SUjPW��HVfvNQKNQ� e>c9S��9Q�VLQ,+-�NM^j^M��NSUM��Ne M^T�VfvNQ�K h£v�c9Sfc9h�VfQ�SUM�7�Q�k4�HW c9K M^KNh�SUQ�c9TUQ�M^K ��;zc9KNk c9K M^KNh�SUQ�c9TUQ�M^K;�EY9VfvM ;�Z�;Lc9KNk M � � Q�;LM^e-bNjPW=M^KN_�Vfv�c�V�VfvNQ�bNSUQ�k�c�VfYRS�TUbEQ�h�M^Q�TLm�kNY=Q�T�v�c�ORQ�c9K�M^e-b�c9h�V�YRKZTUbEQ�h�M^Q�Ta~=l "A��VVfvNM^TLh�YRKNh�j��NTUM^YRK kNQ�bEQ�KNkNTaYRK Y��NSLb�c9SdVfM°c9j�c9K�c9jPW=TUM^TLc9TUT��Ne-b�VfM^YRK Y9[ �9Q�Q�bNM^KN_ �1V�c9KNk � �ah�YRKNTdV£c9KHV�l��Q�V�Y��NS�_RQ�KNQ�Sfc9j]Q,+-�NM^j^M��NSUM��Ne$c9K�c9jPW=TUM^T�TUvNY/�T�Vfv�c�V�VfvNQte>c9S��9Q�V�bNSUM^h�Q�T�h£v�c9KN_RQ>c9T!�Q�j^j]TUY�Vfv�c�VVfvNQ�KNQ� Q,+-�NM^j^M��NSUM��Ne YRK VfvNQte>c9S��9Q�V!�NKNkNQ�S�h�YRKNTUM^kNQ�Sfc�VfM^YRKØM^TzSUQ�c9h£vNQ�k �HW$�9Q�Q�bNM^KN_ �6V9G �1V�� ��;�NKNh£v�c9KN_RQ�k�c9KNk��HW%c9K%M^KNh�SUQ�c9TUQaM^K�� ��G ��; � � �A�vNM^h£v%SUQ�k��Nh�Q�TCQ�;!VfY Q � ; T��Nh£v%Vfv�c�VCM���Q�;CGAM � � Q � ; l� ����� ��������������% %����&'���!(

�F��� ��2X)+.d #.0$&.6�!" � 2 �9'�.6� �H" �*%(2#$&'� VLVfvNQ�Q�KNk Y9[ÆVfvNQ�TUvNYRSdVdnXS��NK bEQ�SUM^Y=k@�4Q�c9h£v YRSU_Hc9KNM^TUe c9h,+-�NM^SUQ�k c-bEYRTUMPVfMPORQ�YRSLKNQ�_Hc�VfMPORQ�c9e-Y��NKHVY9[�KNQ�V��NM^YRe>c9TUT c O l � OUTSV ^aM0`�I � O ^aM0` p��vNQ�SUQ9M M^TÇVfvNQaORQ�h�VfYRS!Y9[�bEYRb��Nj°c�VfM^YRKNT�l ��[�bEYRTUMPVfMPORQ.��VfvNQzKNQ�V�NM^YRe>c9TUT*_RQ�KNQ�Sfc�VfQ�k(�HW�VfvNQ!SUQ�bNSUQ�TUQ�KHV£c�VfMPORQ�YRSU_Hc9KNM^TUe h�c9K �EQ!M^kNQ�KHVfM*��Q�k�c9TY.)0TUbNSUM^KN_Nl ��[4KNQ�_Hc�VfMPORQ.�VfvNQ�KNQ�V:�NM^YRe>c9TUT�M^KNkNM^h�c�VfQ�T�VfvNQ�YRSU_Hc9KNM^TUe � T�h£v�c9KNh�Q�VfY-T��NSdO=MPORQ�VfvNQ�bEQ�SUM^Y=kÄl ?ÙQ�KNYRSUe>c9j^M�7�QaQ�c9h£vYRSU_Hc9KNM^TUe c9T�h�YRKNTUM^TdVfM^KN_tY9[YRKNQ��NKNMPV�Y9[�|DY/�K4}��NM^YRe>c9TUT�c9KNk�h�c9K�VfvNQ�SUQ�[DYRSUQ!�SUMPVfQ

�MPO0G� MPO��

GAMPOc O � � OUTSV ^aM0`�I � O ^aM0` � [DYRS5EHG <JIDBDBDBKI�7�B |8{H}

��VÓM^T�M^KHVfQ�SUQ�TdVfM^KN_ VfY [F�NSdVfvNQ�SÓTUbEQ�h�MP[ÂW VfvNQ>kNM*)0Q�SUQ�KHVfM°c9j�Q,+-��c�VfM^YRKNTÓY9[�bEYRb��Nj°c�VfM^YRKÙ_RSUY/�VfvÄl \=YRe-Q_RQ�KNQ�Sfc9j �NTUQ�[F�Nj�M^KNTUM^_RvHV�M^T�bNSUY�O=M^kNQ�k;�HW

����� ���"!$#&%�#'�"( �\+ -�� � �P� 4 ��> �0� 1 9��� � >&@26- � 6 ) A >&@ � ��� � � � � � � � � � � � 1 � ��1�> � >&@ � 1X>&@ � � � �P� 4 ��> �0� 1 9��� � >&@ > ��� � ��>&@ ��A � 1 �h> �0� 1P��4 A$�[� �

�M V G M VDn� I�M ; G M ;�� ; ^aM V�I�M ;�`1I��� ����MPO G MPO�� O ^aM V�I�M ;�IDBDBDBKI�MPOa`PI��� ����M � G M ��� � ^M V�I�M ;�IDBDBDB�I�M �#TSV�I�M ��`PI

|¹��qH}

�Io

Page 18: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

� @ ����� n� � � � � � 1*�h> ��1�>C��1 � � O � i O g :�� i �- �� 6 ) A >&@ � ��� � � � � � � � �{�2��� � � � � >&@ � 1 >&@ � � � �P� 4 ��> �0� 1 9��� � >&@ > ��� � � >&@ �eA � 1 �h> �0� 1P��4 A$�[� �

�M V G M V�� V ^aM V `1I�M ; G M ;�� ; ^aM V�I�M ;�`PI��� ����MPO G MPO�� O ^aM V�I�M ;DIDBDBDBKI�MPOa`1I��� ����M � G M ��� � ^aM V�I�M ;�IDBDBDBKI�M �#TSV�I�M ��`PB

|¹�R�I}

� @ ����� � O � i O g :�� i ���vNQ�[F�NKNh�VfM^YRK�c9j0[DYRSUe Y9[VfvNQ�bEYRb��Nj°c�VfM^YRKZ_RSUY/�Vfv SUQ�x�Q�h�VfTaY��NS�e-Y=kNQ�j^j^M^KN_�Y9[VfvNQ�Q�h�YRTdW=TdVfQ�e$c9Tac�NKNM^kNM^SUQ�h�VfM^YRK�c9j�[DY=Y=k>h£v�c9M^KÄl���vNQ�bEYRb��Nj°c�VfM^YRK-_RSUY/�VfvZY9[�TUbEQ�h�M^Q�T�EM^T!c )0Q�h�VfQ�k��HWZc9j^j4bEYRb��Nj°c�VfM^YRKNTY9[TUbEQ�h�M^Q�T �(�MPVfv � w E�� ����VLMPV�M^T�M^KNkNQ�bEQ�KNkNQ�KHVLY9[Æc9j^jÄbEYRb��Nj°c�VfM^YRKNT!Y9[TUbEQ�h�M^Q�T����MPVfv� u EUl�F� � $&" �� �*%(/1" � � 2 � � �(" �*%(2#$ - �$&"X)+%(/1'�� � 2 � � �� =2 �& �("#'���*Y�Y���V£c9M^K-c9kNkNMPVfM^YRK�c9j=M^K�[DYRSUe>c�VfM^YRK�YRK�VfvNQ�h£v�c9Sfc9h�VfQ�SUM^TdVfM^h�T]Y9[0bEYRb��Nj°c�VfM^YRKÓ_RSUY/�Vfv(�Q�bNSUY=h�Q�Q�k3�HWM^KHVfSUY=k��Nh�M^KN_ c b�c9Sfc9e-Q�VfSUM^htKNQ�V&�NM^YRe>c9TUT�[F�NKNh�VfM^YRK@�K�c9e-Q�jPW VfvNQ���Y����=n¹`aY��N_Rj°c9T�[F�NKNh�VfM^YRKÄl y��NSc9M^e M^TÓSfc�VfvNQ�S�VfYØh�j°c9SUMP[ÂW VfvNQZbEY9VfQ�KHVfM°c9j�Y9[LY��NS�c9bNbNSUYHc9h£v2c9TÓh�YRe-b�c9SUQ�k VfY VfvNQZe-Y=kNQ�j^T�Y9[�VfvNQ�ÇQ�SUv-�Nj^TdVdn 1*Q�c9SUj!VXW=bEQ |D_RSUY/�Vfv2Y9[�cØTUM^KN_Rj^QZTUbEQ�h�M^Q�T£}�c9KNk2Y9[aVfvNQ; �Y9V���cIn��ÇYRjPVfQ�SUSfc VXW=bEQ |D_RSUY/�VfvM^K c bNSUQ�k�c�VfYRS¹nXbNSUQ�W h�YRKHVfQ��=V�}�l;�*Y [F�NSdVfvNQ�S�TUM^e-bNj^MP[ÂW4�Q%SUQ�TdVfSUM^h�V�Y��NS�c�VUVfQ�KHVfM^YRK VfY [DY=Y=k h£v�c9M^KNTh�YRKNTUM^TdVfM^KN_tY9[Æc�SUQ�TUY��NSUh�Q�c9KNk�VfvNSUQ�Q�TUbEQ�h�M^Q�T�l

��YRKNTUM^kNQ�S�KNY/AVfvNQ�KNQ�V:�NM^YRe>c9TUT![F�NKNh�VfM^YRK

c O ^QSOUTSV�I�Z[Oa`5G=Q�� OUTSV ��^�nZ[O : Z[Oa`�� :���O I |¹�I~R}

�vNQ�SUQ m w�� O w <�� m w�� O w <Óc9KNk���O u m l��*Y>M^KHORQ�TdVfM^_Hc�VfQ�vNY/�VfvNQ�Q�h�YRTdW=TdVfQ�e$kNQ�ORQ�j^YRbNTaY�ORQ�SVfM^e-Q.�EMPVaM^Tah�YRKHORQ�KNM^Q�KHVzVfY%TdV£c9SdV��MPVfv c9K c.���NKNk�c9KHVzSUQ�TUY��NSUh�QÓVfY%TUQ�QÓMP[Çc9KNk vNY/ÒVfvNQÓQ�h�YRTdW=TdVfQ�e�EQ�h�YRe-Q�Tah�SUY/�kNQ�kÄl!��vNQ�K c9h�h�YRSUkNM^KN_-VfY%bNSUYRbEYRTUMPVfM^YRK ��|DMÂ}%�NM^YRe>c9TUTLkNQ�e>c9KNkNTzc9KNk T��NbNbNj^M^Q�Tzc9SUQ_RMPORQ�K;�HW

QSOUTSVXG � O�nZ[O^ � O � � Oa` ��O c9KNk Z[O6G � O�nZ[O� O � � O EHG <JI�@�I �*B |¹��mH}

g +-�NM^j^M��NSfc�VfM^KN_�kNQ�e>c9KNk c9KNk T��NbNbNjPW�[DYRS5�NM^YRe>c9TUT�Y9[]TUbEQ�h�M^Q�T��Óc9KNkØ~ÓW=M^Q�j^kNTLb�c9Sfc9e-Q�VfQ�SUT ^ � ;DI � ��`Tfc�VfM^Td[ÂW=M^KN_

� ;CG M ; � ;[^ � V � � V `[nZ�;M V � VD^ � ; � � ;�`[nZ�V c9KNk � �CG M�� � ��^ � ; � � ;�`[nZ��M ; � ;�^ � � � � ��`[nZ�; B |¹��y�}

��r

Page 19: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

��vNQ�c9TUTUY=h�M°c�VfQ�k Q,+-�NM^j^M��NSUM��Ne kNQ�e>c9KNkNTLc9KNk T��NbNbNj^M^Q�T�c9SUQ9w

Q�9 G � V[nZ�V^ � V � � V ` �DV I Z�V5G � V[nZ�V� V � � V I |¹�Io9cH}

Q6VrG M V � V[nZ�VM ;[^ � V � � V�` I Z�;CG � ;onZ�;� ; � � ; I |¹�Io �4}

Q�; G M ; � ;onZ�;M��[^ � ; � � ;�` I Z��CG � �onZ��� � � � �

B |¹�Io�h�}

��YRe0�NM^KNM^KN_ |¹�IoR} ��|¹�I~R}!c9KNkÙ|8{H}�W=M^Q�j^kNT�VfvNQ�kNM*)0Q�SUQ�KHVfM°c9j0Q,+-��c�VfM^YRKNT�Y9[bEYRb��Nj°c�VfM^YRK%_RSUY/�Vfv

�M VrG M V l � � 9 :��SV poI |¹��rRcH}�M ; G M ; �Je M VM ; � ; h ��� :�� ; � I |¹��r.�4}

�M�� G M�� �Je M ;M�� � � h ��� :�� � � I |¹��r9h�}

�vNQ�SUQ � 9 � G � ��z � � g � � � � � � ��z � g � � � � � ; � G � ��z � g � � � � � �z ���� g � � � � � � � � � � G ��� �z ���� g � � � � � � �z ���� g � � � � � � l\<�NbNbEYRTUQ KNY/>M V_G nZ�9 ��Q�9 G ^ � V � � V ` �DV[nZ�9 �!^ � V[nZ�V `ÓM^TtSUQ�c9h£vNQ�k c9KNk2VfvNQ�SUQ�TUY��NSUh�Q _RQ�VfT

TUh�c9SUh�Q9l ��vNQ�K Q�h�YRTdW=TdVfQ�e'bNSUM^h�Q�TZc9SUQ4�NM^KNkNM^KN_ c9KNk c9h�h�YRSUkNM^KN_ÙVfY bNSUYRbEYRTUMPVfM^YRKÕ�Ü|DM^MÂ}0�NM^YRe>c9TUTkNQ�e>c9KNkNTLc9KNk T��NbNbNj^M^Q�T�c9SUQ�KNY/�_RMPORQ�K��HWEw

QSOUTSVXG � O�nZ[O^ � O � � Oa`��SOUTSV c9KNk Z[O1G � O�nZ[O� O � � O EHG <JI�@�I �*B |¹�IpR}

� _RQ�KNQ�Sfc9j�TUvNYRSdVdnXS��NKÕQ,+-�NM^j^M��NSUM��Ne Y9[�VfvNQ Q�h�YRTdW=TdVfQ�e M^T�c�VUV£c9M^KNQ�kÕc�V TdVfSUM^h�VfjPW bEYRTUMPVfMPORQØbNSUM^h�Q�T^ ��9DI �1V�I ��;�`�Tfc�VfM^Td[ÂW=M^KN_��9CG M V � V[nZ�V^ � V � � V�`[nZ�9 I �6VXG M ; � ;�^ � V � � V `[nZ�;M V � VK^ � ; � � ;�`[nZ�V c9KNk ��;CG M�� � �[^ � ; � � ;�`[nZ��M ; � ;[^ � � � � ��`[nZ�; B |¹��sH}

��vNQ�c9TUTUY=h�M°c�VfQ�k Q,+-�NM^j^M��NSUM��Ne kNQ�e>c9KNkNTLc9KNk T��NbNbNj^M^Q�T�c9SUQ

Q�9 G nZ�9M V I Z�V#G � V[nZ�V� V � � V I |¹��{RcH}

Q6VrG M V � V[nZ�VM ;[^ � V � � V�` I Z�;CG � ;onZ�;� ; � � ; I |¹��{.�4}

Q�; G M ; � ;onZ�;M��[^ � ; � � ;�` I Z��CG � �onZ��� � � � �

I |¹��{9h�}

c9KNk�VfvNQ�bEYRb��Nj°c�VfM^YRKNT�_RSUY/ c9h�h�YRSUkNM^KN_�VfY�VfvNQ�kNM*)0Q�SUQ�KHVfM°c9jÄQ,+-��c�VfM^YRKNT � �Ó|¹��r.�4} ��|¹��r9h�}�c9KNk�M VjG M V � �Je � VM V h � :��SV � |�~9qH}

�vNQ�SUQ � V � G nZ�9 � � ��z � g � � � l� � Á°¬Æ¶8·I­�ºI²³ªz¾9©�µI­�¬�©Uªz¬�·�«£¬Q[ ! ~ �o�£Ê [�5~ � ! Ê�DFE�£¾.K�¸¹­�´ µ�¸¹´³ª�©U¶�¿�´ ¬�·3DFE�G�¾.K�«�µ�ª DFE��¸�KÄ´³¶�©UÑ�ºI´ ã«�² ©dµ�¬*¬�­'DFE�G�¸�KXÀ×Ä·I©U¶8©]¸¹­�¨�¨�©U¶8¯9­�µ�ª�©dµ�¸¹©U¶Ä«�¨�©Æ¸d«�º�¶8©UªL¾�±�¬�·I©Ç¸¹­�µ�¶D¬�«�µ�¬�¶8ºI¯I¯I² ±�»¼ºIµ�¸X¬�´ ­�µ�¶dÊ�»¼­�¨�½�«�² ² ± �� �� ~�� �� ~:Y�»¼­�¨�«�² ²�}�À

�Ip

Page 20: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

|¹��rRcH}Óc9KNk�|�~9qH} ��h�YRe0�NM^KNQ�k �MPVfv�|¹��r.�4}Óc9KNk�|¹��r9h�} ��h�YRe-bNj^Q�VfQ�jPW kNQ�TUh�SUM��EQZVfvNQ k�W=K�c9e-M^h�TY9[�VfvNQ>VfvNSUQ�Q�nXTUbEQ�h�M^Q�TÓ[DY=Y=k h£v�c9M^KÄl$�*YØh�YRe-b�c9SUQ-VfvNQ�TUQZkNM*)0Q�SUQ�KHVfM°c9j�Q,+-��c�VfM^YRKNT�VfY VfvNQ%TdV£c9KNk�c9SUk �Y9V���cIn��ÇYRjPVfQ�SUSfc�bEYRb��Nj°c�VfM^YRKZQ,+-��c�VfM^YRKNT��Q�M^_RKNYRSUQzTUbEQ�h�M^Q�T���c9KNk SUQ��SUMPVfQ-|¹��r.�4}!c9KNk |¹��r9h�}!c9T

�MPO6G � O M�� OUTSV M V T � O :���OUMPO EHGd@�I �*B |�~=�I}

��vNQ�h�YRSUSUQ�TUbEYRKNkNM^KN_6 �Y9V���cIn��ÇYRjPVfQ�SUSfc�Q,+-��c�VfM^YRKNT%�Y��Nj^k�SUQ�c9k � \�M ;�G�� ; V�M ;X:�� ;�;�M ;�M�� c9KNk �M���G�� � V�M ;�M��X:�� ��;�M���I |�~R~R}

�vNQ�SUQ�VfvNQ�� � T�c9SUQ�bEYRTUMPVfMPORQÓb�c9Sfc9e-Q�VfQ�SUT�l0��vNQth�YRe-b�c9SUM^TUYRK Y9[�|�~=�I}ac9KNk |�~R~R}LSUQ�c9kNM^jPW SUQ�ORQ�c9j^T�cT����NTdV£c9KHVfM°c9j]TdVfS��Nh�V��NSfc9jÇc9TdW=e-e-Q�VfSdW#�EQ�V �Q�Q�K �EY9Vfv e-Y=kNQ�j^T�l �XK VfvNQtbNSUQ�TUQ�KHV�e-Y=kNQ�j��0VfvNQtbEYRb��=nj°c�VfM^YRK _RSUY/�VfvÙY9[!VfvNQ-V �Y TUbEQ�h�M^Q�T�M^T�TdVfS��Nh�V��NSfc9j^jPW VfvNQ>Tfc9e-Q>c9KNk +-��c9j^MPV£c�VfMPORQ�jPW TUM^e-M^j°c9SaVfY VfvNQbNSUQ�k�c�VfYRSÆTUbEQ�h�M^Q�TÇm � T]_RSUY/�Vfv�M^K�VfvNQ5 �Y9V���cIn��ÇYRjPVfQ�SUSfc�e-Y=kNQ�j�l "A��VÆVfvNQ�_RSUY/�Vfv�Y9[4VfvNQ!bNSUQ�WÓTUbEQ�h�M^Q�T~�kNM*)0Q�SUT!TUM^_RKNM*��h�c9KHVfjPWtM^K��EY9Vfv%e-Y=kNQ�j^T�l � � ?ÙQaVfvNQ�SUQ�[DYRSUQzh�YRKNh�j��NkNQaVfv�c�VA�Q�v�c�ORQ�T��N_R_RQ�TdVfQ�k�vNQ�SUQc9K�Q���bNj°c9K�c�VfM^YRK�Y9[4bNSUQ�k�c�VfYRS¹nXbNSUQ�WÓbEYRb��Nj°c�VfM^YRK�k�W=K�c9e-M^h�TVfv�c�VÆM^TM^KNh�YRe-b�c�VfM��Nj^QÆn*c9KNkÓvNQ�KNh�Q�h�YRe�nbEQ�VfQ�T*n �MPVfv�VfvNQ�TdV£c9KNk�c9SUk �Y9V���cIn��ÇYRjPVfQ�SUSfc�c9bNbNSUYHc9h£vÄl ��VÆSUQ�e>c9M^KNT�VfY��EQ�TUQ�Q�K�M^K�[F��V��NSUQ�Q�e-bNM^SUM^h�c9j�YRS��%vNY/ �Q�j^jÄY��NSLc9bNbNSUYHc9h£v kNQ�TUh�SUM��EQ�T�kNQ�ORQ�j^YRbNe-Q�KHVfTLM^K�SUQ�c9j¼n��YRSUj^k%Q�h�YRTdW=TdVfQ�e-T�l

\=Q�ORQ�Sfc9j�M^KHVfQ�SUQ�TdVfM^KN_�[DQ�c�V��NSUQ�T � � Y9[4VfvNQ�_RSUY/�Vfvtk�W=K�c9e-M^h�T]h�c9K(�EQ�kNQ�SUMPORQ�kt[DSUYRe |¹��r.�4} �E|¹��r9h�}c9KNk |�~9qH}�l ��YRKNTUM^kNQ�S%��SUTdVÓ|�~9qH}�lÇ`aM*)0Q�SUQ�KHVfM°c�VfM^YRK��MPVfv�SUQ�TUbEQ�h�VLVfYRM V�W=M^Q�j^kNT� �M V� M V G � � V ��^(<F: � V�`Q��M T � V :��SV c9KNk �

; �M V� M ; V G�: � � V � � VQ��^(<F: � V `Q��M T � V g � �V w m B

��j^Q�c9SUjPW�� �M V�[DSUYRe |�~9qH}�M^T�TdVfSUM^h�VfjPW%h�YRKNh�c�ORQ�M^K M V�lÇiLQ�KNh�Q��Q�h�c9j^h,�Nj°c�VfQ�M V � G � VQ� e <F: � V�SV h

c9KNk M � V-� G � V � e <�SV h

�vNQ�SUQ �M V#G ����e������� �M V�c9KNk��vNQ�SUQ{M � V TUYRjPORQ�T�|�~9qH}][DYRS �M V#G m �=M�l Q9lÆVfvNQzbEYRb��Nj°c�VfM^YRK-Y9[�TUbEQ�h�M^Q�T��SUQ�c9h£vNQ�T�cÓj^YRKN_�nXS��NK>Q,+-�NM^j^M��NSUM��Ne$|DTdVfQ�c9k�W%TdV£c�VfQ�}�l���Q�h�c9j^j��=vNY/�Q�ORQ�S,�NVfv�c�V�|�~9qH}ÇM^T!YRKNjPWtO9c9j^M^k-[DYRSnZ�9�� M V(Q�9%�vNM^h£v M^T�Q,+-�NMPO9c9j^Q�KHV�VfY M V ��^ � V � � V ` �DV[nZ�9 �!^ � V[nZ�V `�l �*YtkNQ�VfQ�SUe-M^KNQ�vNY/ �M V!kNQ�bEQ�KNkNTYRK�M V�Y�ORQ�SÓVfvNQZQ�KHVfM^SUQ>kNYRe>c9M^K Y9[�KNYRK=nXKNQ�_Hc�VfMPORQ M V��QZKNQ�Q�k VfY h�YRe0�NM^KNQ |¹��rRcH}�c9KNkÕ|�~9qH} �]c9TM^j^j��NTdVfSfc�VfQ�ktM^K3��_��NSUQzm�l���vNQ �M VXn�[F�NKNh�VfM^YRK-M^T�M^KHORQ�SUTUQ�jPW3�=nXTUv�c9bEQ�k6�MPVfv%c�j^M^KNQ�c9SÇTUQ�_Re-Q�KHV!Y�ORQ�S�VfvNQM^KHVfQ�SdO9c9j l m I�^ � V � � V�` �DV[nZ�9 �!^ � V[nZ�V ` p�l���vNM^T�j^M^KNQ�c9SÇTUQ�_Re-Q�KHV!KNY9V �MPVfvNTdV£c9KNkNM^KN_�VfvNQa_RSUY/�Vfv%h,�NSdORQzM^K� | N ¬�©¹Ë�¬�¾9­�­�Ï�¬�¨�©U«£¬�½!©dµ�¬�­�»�¬�·I©ÇÐ�­�¬�Ï£«£®°Ý�­�² ¬�©d¨�¨�«Ç½!­�ª�©d²�¸d«�µz¾9©Æ»¼­�ºIµ�ªL´ µ�Ú�ºI¨�¨�«f±�DFE�G�G�O,KXÀ� � ×Ä·I©ÆÖ�¨�¶D¬�©UÑ�º�«£¬�´ ­�µa´ µ D^â�â�K0´³¶Ä´ ½!¯I²³«�º�¶8´ ¾I² ©Æ»¼­�¨ K ]¶8´ µ�¸¹©]ºIµ�¾9­�ºIµ�ª�©Uªa¯9­�¯IºI²³«£¬�´ ­�µzÈ�¨�­£¿Ä¬�·L´³¶�´ µ�»¼©U«�¶8´ ¾I² ©�À P�­�¬�©«�²³¶8­Ó¬�·�«£¬�¬�·I©�¯�«�¨�«�½!©¹¬�©d¨�¶ ! �fÊ� ! ! Ê� �z«�µ�ª� ! «�¨�©�«�ª%·I­�¸�¿�·I©d¨�©U«�¶�¬�·I©�¯�«�¨�«�½!©¹¬�©d¨�¶� *�8Ê����Ç«�µ�ª����:D�}9~� f �,K�ª�©U¶�¸¹¨�´ ¾9©a¬�©U¶D¬�«�¾I² ©z¯I¨�­�¯9©d¨8¬�´ ©U¶�­�»¬�·I©z´ µ�ª�´ Ã�´³ª�º�«�²�­�¨�È�«�µI´³¶8½�¶ D¼¿�´ ¬�·����ƾ9©d´ µIÈt¸¹­�½!¯9­�¶8©Uªt­�»Ã£«�¨�´ ­�º�¶�­�¬�·I©d¨¯�«�¨�«�½!©¹¬�©d¨�¶�KXÀ�'B N ¨�´ È�­�¨�­�º�¶Ä¸�·�«�¨�«�¸X¬�©d¨�´ ÌU«£¬�´ ­�µL­�»�¬�·I©]¬�´ ½!©]¯�«£¬�·�«�µ�ªL¬�·I©�¸¹­�µ�ª�´ ¬�´ ­�µ�¶0»¼­�¨*¸¹­�µ�Ã�©d¨�È�©dµ�¸¹©Æ«�¨�©Æ¾9©d±�­�µ�ªL¬�·I©�¶�¸¹­�¯9©­�»�¬�·I©Æ¯I¨�©U¶8©dµ�¬�¯�«�¯9©d¨UÀ

��s

Page 21: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

��_��NSUQ>m�M^T�Q�TUTUQ�KHVfM°c9j^jPW VfvNQ(�ÇQ�SUv-�Nj^TdVdn 1*Q�c9SUjÇ_RSUY/�VfvÙh,�NSdORQ>_RMPO=M^KN_�SUM^TUQ�VfY c j^YR_RM^TdVfM^hÓbEYRb��Nj°c�VfM^YRKh,�NSdORQ9l >LY9VfQ.��vNY/�Q�ORQ�S%Vfv�c�V-VfvNQ;�ÇQ�SUv-�Nj^TdVdn 1*Q�c9SUjLh,�NSdORQØM^T>c9K c9k vNY=h c9bNbNSUYHc9h£v [DYRS>c TUM^KN_Rj^QM^TUYRj°c�VfQ�k TUbEQ�h�M^Q�T�l �XK2h�YRKHVfSfc9TdVI��vNQ�SUQZVfvNQZQ,+-��c�VfM^YRKNT |¹��rRcH}�c9KNkA|�~9qH}Óc9SUQZkNQ�SUMPORQ�k2Sfc�VfvNQ�SÓVfv�c9Kc9TUT��Ne-Q�k M^K cÓVfvNSUQ�Q�nXTUbEQ�h�M^Q�TLe-Y=kNQ�j�l �0�

M^_��NSUQ�m�w 1*YRb��Nj°c�VfM^YRK�_RSUY/�Vfv�Y9[TUbEQ�h�M^Q�T��

?�MPVfv M V�TUQ�V�h�YRKNTdV£c9KHV�M^K |¹��r.�4} �M ;�h�c9K �EQ%SUQ�c9kNM^jPW TUQ�Q�K VfY kNQ�bEQ�KNk YRK M ;�M^K c TUM^e-M^j°c9S!c�W c9T �M VtkNQ�bEQ�KNkNT%YRK M V�l ��vNQ Tfc9e-Q vNYRj^kNTt[DYRS �M��6�vNQ�K M ;%M^T>c9TUT��Ne-Q�k VfY �EQ h�YRKNTdV£c9KHV�l`aM*)0Q�SUQ�KHVfM°c�VfM^YRKZY9[�|¹��r.�4}!c9KNk |¹��r9h�} �NSUQ�TUbEQ�h�VfMPORQ�jPW��NW=M^Q�j^kNT

� �MPO� MPO G ^aMPOUTSV � Oa` � ��^(<F: � Oa`Q��M T � O :���O EHGd@�I �*I

�; �MPO

� M ;O G :,^aMPOUTSV � Oa`�� � � O ��^(<F: � Oa` �DM T � V g � i�O w m EHGd@�I �*I�vNM^h£v TUvNY/�TaVfv�c�V �MPOM^TLc-TdVfSUM^h�VfjPWZh�YRKNh�c�ORQ�[F�NKNh�VfM^YRK Y9[fMPOXl �YRSLc9KHW _RMPORQ�K MPOUTSV!VfvNQ�e>cI��M^e0�NeM^T

�MPO*^aMPOUTSV�`#G=MPOUTSV � � O � e <F: � O��O h EHG]@�I �*I

c9KNk�VfvNQ�j^YRKN_�nXS��NKZQ,+-�NM^j^M��NSUM��Ne Y9[TUbEQ�h�M^Q�Tz~�c9KNk m ^ �M ;CG �M��CG m `�M^T�SUQ�c9h£vNQ�k c�VM �O ^aMPOUTSV�`5GAMPOUTSVQ� � O � e <��O h

EHGd@�I �*B��j^Q�c9SUjPW���VfvNQah�c9SUSdW=M^KN_Óh�c9b�c9h�MPVXW-Y9[�TUbEQ�h�M^Q�TCEM^T�bNSUYRbEYRSdVfM^YRK�c9j�VfY�VfvNQabEYRb��Nj°c�VfM^YRK-Y9[�TUbEQ�h�M^Q�TCES:�<Rl� c §N©¹¬�·I´ ÈL«�µ�ªz×�¶�¸�·I´ ¨�·�«�¨8¬ D^â�ã�ãME�K0«�²³¶8­�ª�©d¨�´ Ã�©Ç«�¯9­�¯IºI²³«£¬�´ ­�µ�È�¨�­£¿Ä¬�·z¸¹ºI¨�Ã�©Æ­�»�«�¶8´ µIÈ�² ©Ç¶8¯9©U¸¹´ ©U¶�¶8·�«�¯9©Uªa©¹ËI«�¸X¬�² ±

«�¶¬�·�«£¬]´ µ�Ö�È�ºI¨�©%OIÀ!Å0º�¬Ç´ µ�¬�·I©d´ ¨]­�µI©¹®Â¶8¯9©U¸¹´ ©U¶½!­�ª�©d²�¬�·I©�«�² ² ­�¸d«£¬�´ ­�µ�´³¶]ª�¨�´ Ã�©dµ�¾�±�¸¹­�µIÈ�©U¶D¬�´ ­�µ�¨�«£¬�·I©d¨¬�·�«�µÓ¾�±¯I¨�´³¸¹©U¶dÀ

��{

Page 22: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

�F��� � �9)+.6�!%(/1" � � 2 � � �(" �*%(2#$ - �$&"X)+%(/1'�� � 2 � � �� =2 �& �("#'��>LY/ �QÇV��NSUK�VfY�VfvNSUQ�QÇK-�Ne-Q�SUM^h�c9jRQ��Nc9e-bNj^Q�T �vNM^h£v�c9SUQ]h�c9j^h,�Nj°c�VfQ�k��MPVfv�VfvNQ]vNQ�j^b�Y9[=VfvNQ]h�YRe-b���VfQ�SbNSUYR_RSfc9e � c�VfvNQ�e>c�VfM^h�c�l � � �XK VfvNQ�TUQÓQ��Nc9e-bNj^Q�TaVfvNQÓb�c9Sfc9e-Q�VfQ�SUTzc9SUQ�h£vNYRTUQ�K c9Ta[DYRj^j^Y/�T�w �DVFG <��nZ�9�G]@ mJmJmJmJmJmJm �fnZ�V#GW< mJm �5nZ�;CGW< m �5nZ��CGW<�� � O0G � O0G m B���[DYRSLc9j^j6EfG�<JI�@�I ��� �SV#GW< m � � ;CGW<��c9KNk � � G]@=l����� �`� �� D) % ?ÙQzTUQ�V!VfvNQzM^KNMPVfM°c9jNbEYRb��Nj°c�VfM^YRK-TdVfY=h��T�c�V M VD^ m `5G�< mJm ��M ;[^ m `5G�< m c9KNk_M���^ m `#G<Rl�\=M^KNh�Q M V w � � g � � � ��z� ��z G�� mJmJmJmJm VfvNQÓSUQ�TUY��NSUh�QÓM^Tac.���NKNk�c9KHV�c9KNk VfvNQÓbEYRb��Nj°c�VfM^YRK _RSUY/�Vfv M^T_RMPORQ�K;�HW

�M VrG � m M V�I |�~9mRcH}

�M ; G M ; <���B �*<J<�� e M VM ; h 9�� � : <����RI |�~9m.�4}

�M�� G M�� <JB����*<J<�� e M ;M�� h 9�� � : @��RB |�~9m9h�}

��vNQ j^Q�[ÂVtb�c9KNQ�j^T-Y9[ ��_��NSUQ�T>y�n¹r M^j^j��NTdVfSfc�VfQ>VfvNQ _RSUY/�Vfv k��NSUM^KN_ VfvNQ�VfM^e-Q�M^KHVfQ�SdO9c9j l m I m B @ m � ����p�l�XKNMPVfM°c9j^jPWÙc9j^j!bEYRb��Nj°c�VfM^YRKNT�_RSUY/ TUj^Y/�jPWÜc9KNk2VfvNQ�K �Q Y��NTUQ�SdORQ c9K c9bNbNSUY���M^e>c�VfQ�jPW Q���bEYRKNQ�KHVfM°c9jSfc9bNM^kt_RSUY/�VfvÄl �SUYRe G m VfY � G m B @ m � ���aVfvNQLbEYRb��Nj°c�VfM^YRK�Y9[0TUbEQ�h�M^Q�TL�Lv�c9T�M^KNh�SUQ�c9TUQ�kt[DSUYRe ��qRqVfYZyHqRqRqRqRq�l�\=M^KNh�Q M V&G�� mJmJmJmJm M^T�c��EY��NKNk�c9SdW bEYRM^KHVzY9[�VfvNQ�SUQ�_RM^e-QÓc�V��vNM^h£vØVfvNQ�SUQ�TUY��NSUh�QtM^Tc.���NKNk�c9KHVI�4bNSUM^h�Q�T�V£c.�9Q�Y�ORQ�S�VfvNQ�h�YRKHVfSUYRj�Y9[ÆQ�h�YRTdW=TdVfQ�e$c9j^j^Y=h�c�VfM^YRK>TUvNMP[ÂVfM^KN_ÓVfvNQ�Q�h�YRTdW=TdVfQ�e [DSUYRec.���NKNk�c9KNh�QaVfYÓTUh�c9SUh�MPVXWRl ��V!M^T�M^KHVfQ�SUQ�TdVfM^KN_�VfYÓY��NTUQ�SdORQzVfv�c�V!M^K>Y��NS!Q��Nc9e-bNj^Q��aVfvNQzbEYRb��Nj°c�VfM^YRKNT�Y9[TUbEQ�h�M^Q�T���c9KNk ~�_RSUY/Õ[8c9TdVfQ�S�Vfv�c9K�VfvNQ�bEYRb��Nj°c�VfM^YRK%Y9[TUbEQ�h�M^Q�TLm�l � V G � �Q�v�c�ORQ9wM V � � � G�� mJmJmJmJm u M ; � � � G�� m � m @�B < u M�� � � � G����!B <�� m �!B

0.05 0.1 0.15 0.2

25000

50000

75000

100000

125000

150000

175000

K*�7N � P

0.5 1 1.5 2

7× 106

8× 106

9× 106

1× 107

K*�7N � P

M^_��NSUQ�yNw 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�T���M^KZQ��Nc9e-bNj^Q��

� � ×Ä·I©]¯I¨�­�È�¨�«�½Ù»¼­�¨*¶8´ ½�ºI²³«£¬�´ ­�µ�¶0´³¶�«fã«�´ ²³«�¾I² ©*»¼¨�­�½ ¬�·I©Ç«�º�¬�·I­�¨�¶0ºI¯9­�µz¨�©UÑ�ºI©U¶D¬UÀ

~9q

Page 23: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

0.05 0.1 0.15 0.2

5000

10000

15000

20000

K ! N � P

0.5 1 1.5 2

2× 106

4× 106

6× 106

8× 106

K ! N � P

M^_��NSUQ�o=w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�Ta~�M^KZQ��Nc9e-bNj^Q��

0.05 0.1 0.15 0.2

10

20

30

40

50

K hN � P

2 4 6 8

1× 106

2× 106

3× 106

4× 106

5× 106

K hN � P

M^_��NSUQ�r�w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�TLmtM^KZQ��Nc9e-bNj^Q��

?�vNQ�K VfvNQ Q�h�YRTdW=TdVfQ�e M^TtTUh�c9SUh�Q.�!VfvNQ bEYRb��Nj°c�VfM^YRKÜY9[zTUbEQ�h�M^Q�T � _RSUY/�T>c9h�h�YRSUkNM^KN_ VfY VfvNQkNM*)0Q�SUQ�KHVfM°c9jÄQ,+-��c�VfM^YRK

�M V#G=M V �*<��o@J@�B � e <M V h 9�� � : < m � B |�~�y�}

�YRS!VfvNQ�Y9VfvNQ�S�TUbEQ�h�M^Q�T�VfvNQ�kNM*)0Q�SUQ�KHVfM°c9j0Q,+-��c�VfM^YRKNT�|�~9m.�4}!c9KNk |�~9m9h�}�TdVfM^j^jÄc9bNbNjPWRl

��vNQ�SUM^_RvHVLb�c9KNQ�j^TLY9[ ��_��NSUQ�TaytVfvNSUY��N_Rv rtM^j^j��NTdVfSfc�VfQzVfvNQ�h�YRKHVfM^K-�NM^KN_-_RSUY/�Vfv Y9[ÆVfvNQ�bEYRb��=nj°c�VfM^YRKNTaY9[�c9j^jTUbEQ�h�M^Q�T�M^K VfvNQ�TdV£c�VfQ�Y9[�TUh�c9SUh�MPVXWØc9KNk VfvNQ�W TUvNY/ VfvNQÓbEYRb��Nj°c�VfM^YRKNTah�YRKHORQ�SU_RM^KN_ZVfYVfvNQ�M^S�TdVfQ�c9k�W�TdV£c�VfQ�j^Q�ORQ�j^T

M � V G�< �o< m�� u M �; G��*B ��� m �J@O�o< m�� u M �� G���B � m ��� � �o< m�� B��YRKNh�Q�b�V���c9j^jPW-VfvNQ�j^Q�[ÂV�c9KNk�SUM^_RvHV�b�c9KNQ�j^T!Y9[ ��_��NSUQ�y-c9SUQzTUQ�_Re-Q�KHVfT�Y9[cÓTUM^KN_Rj^QzkNM°c9_RSfc9e c9KNkZVfvNQTfc9e-Q�M^TLVfS��NQ�[DYRS�VfvNQ�V �Y%kNM°c9_RSfc9e-T�h�YRKHV£c9M^KNQ�k M^K;��_��NSUQ�T�o>c9KNk r�l:��vNQ�SUQ�c9TUYRK [DYRSLbNSUQ�TUQ�KHVfM^KN_Vfv�c�V]TUM^KN_Rj^Q!kNM°c9_RSfc9eÒM^KÓV �Y�b�c9SdVfT]M^TVfY�Q�e-bNj^Y�W�kNM*)0Q�SUQ�KHVÇTUh�c9j^Q�T]YRK �EY9Vfv-cI��Q�TÆ[DYRSÆM^e-bNSUY�O=M^KN_aVfvNQM^j^j��NTdVfSfc�VfM^YRK-Y9[�VfvNQzTUM^KN_Rj^QzkNM°c9_RSfc9e � T�h,�NSdO9c�V��NSUQ9l="A��V�Q�ORQ�K��MPVfvNY���V�b���VUVfM^KN_ÓVfvNQ�b�c9SdVfT�VfYR_RQ�VfvNQ�SMPV�M^T�Q�c9TdW VfY TUQ�Q>Vfv�c�VÓY��NS�_RSUY/�Vfv h,�NSdORQ�T�M^KÙQ��Nc9e-bNj^Q �Zc9SUQ>j^YR_RM^TdVfM^hth,�NSdORQ�T +-�NMPVfQ>TUM^e-M^j°c9SzVfYVfvNQ�h,�NSdORQLM^e-bNj^M^Q�k0�HW�VfvNQ�_RQ�KNQ�Sfc9j^M�7�Q�k �ÇQ�SUv-�Nj^TdVdn 1*Q�c9SUj4Q,+-��c�VfM^YRKtM^K-c�YRKNQ�nXTUbEQ�h�M^Q�T¹nXe-Y=kNQ�j�| ��YRTUQ�K��{Rs9y�}�c9KNk c9j^jÄh,�NSdORQ�T�VfYR_RQ�VfvNQ�S�SUQ�bNSUQ�TUQ�KHVLVfvNQ�h�c9TUQ�Y9[h�Y=Q���M^TdVfQ�KNh�Q9l

~=�

Page 24: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

0.05 0.1 0.15 0.2

0.008

0.0085

0.009

0.0095

�[ ! N � P

0.05 0.1 0.15 0.2

0.002

0.004

0.006

0.008

0.01

[�hN � P

M^_��NSUQ�p=w=��v�c9KN_RQ�TLY9[*VfvNQ�b�c9Sfc9e-Q�VfQ�SUT � ;ac9KNk � �

0.5 1 1.5 2

18

20

22

24

�GF$N � P

0.5 1 1.5 2

0.02

0.04

0.06

0.08

�o�7N � P

1 2 3 4 5 6

0.01

0.02

0.03

0.04

0.05

0.06

� ! N � P

M^_��NSUQ�s�w=��v�c9KN_RQ�TLY9[*VfvNQ�VfQ�SUe-T�Y9[*VfSfc9kNQ���9/��6V�c9KNk ��;� TUTUY=h�M°c�VfQ�kÙVfY�VfvNQ>_RSUY/�Vfv TUh�Q�K�c9SUM^YRT�Y9[!VfvNQ(��_��NSUQ�T�y VfvNSUY��N_Rv r c9SUQ-VfvNQ(��_��NSUQ�T�p c9KNk

s>Vfv�c�V�bNSUY�O=M^kNQÓM^K�[DYRSUe>c�VfM^YRK c.�EY���VzVfvNQÓh£v�c9KN_RQ�M^K VfM^e-Q�Y9[ÇVfvNQÓQ�KNkNYR_RQ�KNY��NT�b�c9Sfc9e-Q�VfQ�SUT � ;/� � �c9KNk VfvNQ�VfQ�SUe-TLY9[ÆVfSfc9kNQ ��9I���6V�����;/�ESUQ�TUbEQ�h�VfMPORQ�jPW�� �vNM^h£v h�c9K#�EQ�M^KHVfQ�SUbNSUQ�VfQ�kØc9Tae-Q�c9T��NSUM^KN_tVfvNQbNSUQ�k�c�VfM^YRK�SUM^T��Ø|DTUQ�Q�c.�EY�ORQ�}�l �YRSUe>c9j^jPWtVfvNQ�bNSUQ�k�c�VfM^YRK�SUM^T��>O9c9SUM°c.�Nj^Q�T�c9SUQ�TUbEQ�h�M*��Q�k c9T

��9CG M V� mJmJmJmJm I �6VXG � ;CG M ;< m M V c9KNk ��;�G � ��G M��< m M ; B |�~RoR}

��VÓM^T�M^KHVfQ�SUQ�TdVfM^KN_ VfY Y��NTUQ�SdORQ%Vfv�c�V0�EY9Vfv � ;tc9KNk � ��c9SUQ%kNQ�h�SUQ�c9TUM^KN_ M^K VfM^e-Q-M^e-bNjPW=M^KN_ZVfv�c�V�VfvNQbEYRb��Nj°c�VfM^YRKZY9[ÆTUbEQ�h�M^Q�T���_RSUY/�TLe-YRSUQ�Sfc9bNM^kNjPW>Vfv�c9K VfvNQ�bEYRb��Nj°c�VfM^YRK�Y9[ÆTUbEQ�h�M^Q�Tz~0�vNM^h£v M^K�V��NSUK_RSUY/�T%e-YRSUQ Sfc9bNM^kNjPW Vfv�c9K VfvNQ bEYRb��Nj°c�VfM^YRK2Y9[�TUbEQ�h�M^Q�T�m�l ?�vNQ�K VfvNQ SUQ�TUY��NSUh�Q M^T>TUh�c9SUh�Q VfvNQVfQ�SUe-TzY9[ÇVfSfc9kNQÓSUQ�x�Q�h�V�TUh�c9SUh�MPVXWØc9KNk c.���NKNk�c9KNh�Q�Y9[�TUbEQ�h�M^Q�T��NM^YRe>c9TUT�l M^_��NSUQÓsZTUvNY/�TzVfv�c�V�c9j^jVfQ�SUe-TzY9[ÇVfSfc9kNQ�M^KNh�SUQ�c9TUQÓbNSUYR_RSUQ�TUTUMPORQ�jPWØc�V���SUTdVI�ÄVfvNQ�KØVfvNQ�W _RSUY/ c�V�kNQ�h�j^M^KNM^KN_%Sfc�VfQ�T��NKHVfM^j*VfvNQ�WQ�ORQ�KHV���c9j^jPW SUQ�c9h£v VfvNQ�M^SzTdVfQ�c9k�WØTdV£c�VfQ�j^Q�ORQ�j^T�l(��YRe-b�c9SUM^KN_6��_��NSUQ-pZc9KNk s%M^KØh�YRe0�NM^K�c�VfM^YRK4�MPVfv|�~RoR} �QLh�YRKNh�j��NkNQ�Vfv�c�V�VfvNQLTUbEQ�Q�k>Y9[ÄbEYRb��Nj°c�VfM^YRKt_RSUY/�Vfv>kNQ�bEQ�KNkNT�YRK(�vNQ�VfvNQ�S�VfvNQLQ�h�YRTdW=TdVfQ�e M^T

~R~

Page 25: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

c.���NKNk�c9KHVzYRS�TUh�c9SUh�Q9l��XK h�c9TUQ�VfvNQ�SUQ�TUY��NSUh�Q�M^TLTUh�c9SUh�Q�VfvNQ�bEYRb��Nj°c�VfM^YRK�Y9[ÆTUbEQ�h�M^Q�Tzm-_RSUY/�T�[8c9TdVfQ�SVfvNQ�K VfvNQ�bEYRb��Nj°c�VfM^YRK�Y9[]TUbEQ�h�M^Q�T�~ �vNM^h£v M^K V��NSUK _RSUY/�Tae-YRSUQ�Sfc9bNM^kNjPW%Vfv�c9K VfvNQ�bEYRb��Nj°c�VfM^YRK�Y9[TUbEQ�h�M^Q�T��Rl

����� �`� �� �����(�� ��% �XK2Q��Nc9e-bNj^Q � c9j^j!bEYRb��Nj°c�VfM^YRKNTÓV��NSUKNQ�k Y���V-VfY �EQ�TdVfSUM^h�VfjPW M^KNh�SUQ�c9TUM^KN_YRK VfvNQ�M^S�b�c�Vfv VfY/!c9SUkNTtVfvNQ�TdVfQ�c9k�W TdV£c�VfQ9l ��VtTUQ�Q�e-TtK�c�V��NSfc9j�VfY c9T�� �vNQ�VfvNQ�S�VfvNM^TÓ[DQ�c�V��NSUQ�M^T_RQ�KNQ�SUM^hÓ[DYRSaVfvNQ�e-Y=kNQ�jÆc�V�v�c9KNkÄl �XKHV��NMPVfMPORQ�jPW��ÄYRKNQ�e-M^_RvHVzQ���bEQ�h�V�c%bNSUQ�k�c�VfYRS�bEYRb��Nj°c�VfM^YRK VfY��EQTdVfSUQ�TUTUQ�k>c9KNk�vNQ�KNh�Q�VfYzkNQ�h�j^M^KNQ.�RY�ORQ�S]TUYRe-Q�VfM^e-Q�M^KHVfQ�SdO9c9j��Rc�VÆj^Q�c9TdV��vNQ�KNQ�ORQ�SÇMPVfTÆbNSUQ�WÓbEYRb��Nj°c�VfM^YRKM^TzT�� �-h�M^Q�KHVfjPW TUe>c9j^j�l!�*Y�Q���bNj^YRSUQÓVfvNM^Tzh�YRKM8UQ�h�V��NSUQ �Q�bNSUY�O=M^kNQÓV �Y�e-YRSUQÓQ��Nc9e-bNj^Q�TzVfv�c�V�kNM*)0Q�S[DSUYRe Q�cI�Nc9e-bNj^Q-��M^K Vfv�c�V�|DMÂ}!VfvNQÓQ�h�YRTdW=TdVfQ�e M^Tac9j^SUQ�c9k�W TUh�c9SUh�QÓM^K VfvNQ�M^KNMPVfM°c9j�TUMPV���c�VfM^YRK | �vNM^h£vTUQ�SdORQ�T�YRKNjPWÓVfY�TUM^e-bNj^MP[ÂW�VfvNQaQ���bEYRTUMPVfM^YRK4}]c9KNk-Vfv�c�V�|DM^MÂ}ÆYRKNQLYRS=�EY9Vfv>bNSUQ�k�c�VfYRS�TUbEQ�h�M^Q�T�v�c�ORQzj°c9SU_RQbEYRb��Nj°c�VfM^YRKNT!SUQ�j°c�VfMPORQzVfY�VfvNQ�M^S�bNSUQ�W=T�l

�XK Q��Nc9e-bNj^QZ~ZVfvNQ%bEYRb��Nj°c�VfM^YRKNT�c�V G m c9SUQ-TUQ�V M VD^ m ` G � mJmJmJmJm �vM ;[^ m ` G < mJmJmJm c9KNkM��[^ m `5G�< mJmJmJmJm l5y��HO=M^Y��NTUjPW�VfvNQabEYRb��Nj°c�VfM^YRKtY9[�TUbEQ�h�M^Q�T�~�M^TÇORQ�SdW>TUe>c9j^j�M^K>h�YRe-b�c9SUM^TUYRK-VfY�VfvNYRTUQY9[TUbEQ�h�M^Q�T���c9KNk m�l y �M^KN_�VfY-MPVfT�TUe>c9j^j0bEYRb��Nj°c�VfM^YRK@��TUbEQ�h�M^Q�Tz~&�M^j^jÄT��NbNbNjPWZYRKNjPW%j^MPVUVfj^Q �NM^YRe>c9TUTM^K VfvNQ c9_R_RSUQ�_Hc�VfQ��vNM^j^QZVfvNQ�kNQ�e>c9KNk2Y9[zTUbEQ�h�M^Q�T>m M^T�vNM^_Rv2k��NQZVfY MPVfTtj°c9SU_RQZbEYRb��Nj°c�VfM^YRKÄl � Tc h�YRKNTUQ,+-�NQ�KNh�QZVfvNQ>Q,+-�NM^j^M��NSUM��Ne bNSUM^h�Q ��;ÓM^T�vNM^_Rv c9KNkÙVfvNQ>Q�h�YRTdW=TdVfQ�e c�VUV£c9M^KNT�c9KÙQ,+-�NM^j^M��NSUM��Nec�V��vNM^h£vAj^MPVUVfj^Q4�NM^YRe>c9TUT�Y9[ÓTUbEQ�h�M^Q�T ~ M^TZVfSfc9kNQ�kÄl M^_��NSUQ�T�{In£�R� M^j^j��NTdVfSfc�VfQ VfvNQ M^e-bNj^M^h�c�VfM^YRKNTYRK VfvNQ>bEYRb��Nj°c�VfM^YRK k�W=K�c9e-M^h�T�l�?�vNM^j^Q�VfvNQ>bEYRb��Nj°c�VfM^YRKNT�Y9[�TUbEQ�h�M^Q�T%�%c9KNkÜ~�Q���vNM��NMPVÓc j^YR_RM^TdVfM^h_RSUY/�Vfv@�Æc9T�M^KÙQ��Nc9e-bNj^Q����*VfvNQ-bEYRb��Nj°c�VfM^YRK Y9[�TUbEQ�h�M^Q�TÓm�kNSUYRbNT�TUv�c9SUbNjPWØ[DSUYRe M��[^ m ` G � mJmJmJmJmVfY M���^ m B m �J` G������o@��!B <�����VzMPVLSUQ�h�Y�ORQ�SUT�c�[ÂVfQ�S G m B m �=l%��vNQ&�NM^YRe>c9TUT�Y9[]TUbEQ�h�M^Q�T�~tv�c9T:�EQ�h�YRe-Qj^Q�TUT�TUh�c9SUh�Qac9KNktVfvNQLSUQ�bNSUQ�TUQ�KHV£c�VfMPORQaYRSU_Hc9KNM^TUe Y9[ÄTUbEQ�h�M^Q�T�m�h�c9K>c )0YRSUktVfY�kNQ�e>c9KNk-e-YRSUQ%�NM^YRe>c9TUTY9[ÇTUbEQ�h�M^Q�T�~tk��NQ�VfYZc-j^Y/�Q�SzbNSUM^h�Q���; �MPVfv VfvNQ�h�YRKNTUQ,+-�NQ�KNh�Q�Vfv�c�VaVfvNQ�bEYRb��Nj°c�VfM^YRK Y9[ÇTUbEQ�h�M^Q�T�mM^KNh�SUQ�c9TUQ�T�[DYRS u m B m �=l

0.5 1 1.5 2

7× 106

8× 106

9× 106

1× 107

K*�N � P

M^_��NSUQ�{�w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�T���M^KZQ��Nc9e-bNj^Q�~

�XK Y��NS5��K�c9j*Q��Nc9e-bNj^Q�VfvNQ�bEYRb��Nj°c�VfM^YRK Y9[]TUbEQ�h�M^Q�T���M^TLSUQ�j°c�VfMPORQ�jPWZj^Y/Òc9Tah�YRe-b�c9SUQ�k VfY-VfvNQbEYRb��Nj°c�VfM^YRKNT!Y9[TUbEQ�h�M^Q�Tz~�c9KNk m�l ?ÙQ�v�c�ORQ�TUQ�VsM VD^ m `5G�� mJmJmJmJm �*M ;[^ m `#G � mJmJmJmJmJm c9KNk M��[^ m `#G� mJmJmJmJmJm l��XKNk��Nh�Q�k �HW �NM^YRe>c9TUT�kNQ�e>c9KNkNT�c9KNkÙT��NbNbNj^M^Q�T�SUQ�TUbEYRKNkNM^KN_ VfY�VfvNQ%c9bNbNSUYRbNSUM°c�VfQtbNSUM^h�Q

~9m

Page 26: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

0.5 1 1.5 2

2× 106

4× 106

6× 106

8× 106

K ! N � P

M^_��NSUQÓ��q�w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�Tz~ÓM^K�Q��Nc9e-bNj^Q�~

0.02 0.04 0.06 0.08 0.1 0.12

98000

100000

102000

104000

K hN � P

1 2 3 4 5

1× 106

2× 106

3× 106

4× 106

5× 106

K hN � P

M^_��NSUQÓ�R�Rw 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�Tam�M^K�Q��Nc9e-bNj^Q�~

TUM^_RK�c9j^T,�9VfvNQ�TUe>c9j^j�bEYRb��Nj°c�VfM^YRKÓY9[0TUbEQ�h�M^Q�T���VfSUM^_R_RQ�SUTÆkNY/�K !c9SUk%c9kM8��NTdVfe-Q�KHVfTÇY9[EVfvNQ�bEYRb��Nj°c�VfM^YRKNTY9[ÇTUbEQ�h�M^Q�T�~>c9KNkØm%c9TaM^j^j��NTdVfSfc�VfQ�k M^K VfvNQÓj^Q�[ÂVab�c9KNQ�j^TaY9[���_��NSUQ�TÓ��m%c9KNk ��yNl:��vNQÓbEYRb��Nj°c�VfM^YRK Y9[TUbEQ�h�M^Q�Tt~�SUQ�h�Y�ORQ�SUTtc�[ÂVfQ�S G m B <%c9KNkÙVfvNQ>bEYRb��Nj°c�VfM^YRK Y9[�TUbEQ�h�M^Q�T�m c9j^TUY SUQ�h�Y�ORQ�SUT,� �MPVfv TUYRe-QVfM^e-QzkNQ�j°c�W��4c�[ÂVfQ�S G m B ��l

0.5 1 1.5 2

7× 106

8× 106

9× 106

1× 107

K*�N � P

M^_��NSUQÓ�I~=w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�T���M^K�Q��Nc9e-bNj^Q�m

�*Y�T��Ne �Nb@�HQ��Nc9e-bNj^Q�TÇ~zc9KNktmzh�YRK���SUe-Q�k�Y��NSÆh�YRKM8UQ�h�V��NSUQ!Vfv�c�V]bNSUQ�k�c�VfYRSÆbEYRb��Nj°c�VfM^YRKNTe>c�WkNQ�h�j^M^KNQ |ÂVfQ�e-bEYRSfc9SUM^jPWN} �vNQ�KÜj^MPVUVfj^QtbNSUQ�W �NM^YRe>c9TUT�M^T�c�O9c9M^j°c.�Nj^Q�[DYRS�[DQ�Q�kNM^KN_Nl �XK Q��Nc9e-bNj^Q�~��QY��NTUQ�SdORQ�k>Vfv�c�VÇVfvNQLbNSUQ�k�c�VfYRSÇTUbEQ�h�M^Q�T�m�V£c.�9Q�T!c�kNM^btY/�M^KN_�VfY�VfvNQ�TUb�c9SUTUQaT��NbNbNjPWtY9[0bNSUQ�W(�NM^YRe>c9TUT|DTUbEQ�h�M^Q�TÇ~R}�l�"A��VVfvNQ�_RSUQ�c�V]c9bNbEQ�VfMPVfQ�Y9[�VfvNQ!bEYRb��Nj^Y��NT*TUbEQ�h�M^Q�T]makNY=Q�TUK � V]SUQ�T��NjPVÆM^K�Y�ORQ�SUv�c9SdORQ�TdVfM^KN_MPVfT�bNSUQ�W�TUbEQ�h�M^Q�T~=l���vNQÇj°c�VUVfQ�SÄQ���vNM��NMPVfT�e-YRKNY9VfYRKNY��NTÄbEYRb��Nj°c�VfM^YRK�_RSUY/�VfvÄlg�Nc9e-bNj^Q]m�M^T�kNM*)0Q�SUQ�KHVM^K%Vfv�c�V�TUbEQ�h�M^Q�TL~ÓM^T��NKNkNQ�S�TdVfSUQ�TUT�Y9[cÓTUe>c9j^j0T��NbNbNjPW%Y9[*bNSUQ�W��NM^YRe>c9TUT�|DTUbEQ�h�M^Q�T��I} �vNM^h£v�SUQ�T��NjPVfTM^KØc-VfQ�e-bEYRSfc9SdW kNQ�h�j^M^KNQÓY9[ÇbEYRb��Nj°c�VfM^YRK ~=l � T�c%SUQ�T��NjPVzY9[]VfvNM^TzkNQ�h�j^M^KNQ.�0TUbEQ�h�M^Q�T�m � TzbEYRb��Nj°c�VfM^YRK

~�y

Page 27: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

0.1 0.2 0.3 0.4 0.5

4× 106

5× 106

6× 106

K ! N � P

0.5 1 1.5 2 2.5 3

8.2× 106

8.3× 106

8.4× 106

8.5× 106

8.6× 106

K ! N � P

M^_��NSUQÓ��m�w 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�Tz~ÓM^K�Q��Nc9e-bNj^Q�m

0.2 0.4 0.6 0.8

2.7× 106

2.8× 106

2.9× 106

3.1× 106

3.2× 106

�K hN � P

1 2 3 4 5 6 7

3.5× 106

4.5× 106

5× 106

K hN � P

M^_��NSUQÓ��yNw 1*YRb��Nj°c�VfM^YRKZ_RSUY/�Vfv Y9[TUbEQ�h�M^Q�Tam�M^K�Q��Nc9e-bNj^Q�m

c9j^TUYZTUvNSUM^K���T��MPVfv c%TUe>c9j^j*VfM^e-Q�j°c9_Zc9KNk Q���vNM��NMPVfTzbEYRTUMPVfMPORQÓ_RSUY/�Vfv Sfc�VfQ�T�c9_Hc9M^KØc�[ÂVfQ�SzSUQ�h�Y�ORQ�SdWY9[MPVfT�bNSUQ�WZTUbEQ�h�M^Q�Tz~=l ��vNQ�VfM^e-Q�j°c9_�_RMPORQ�TLcth�j^Q�c9S�M^KNkNM^h�c�VfM^YRKZSUQ�_Hc9SUkNM^KN_�h�c.�NTUQ�c9KNk Q�)0Q�h�V�l=��vNQkNQ�h�j^M^KNQLY9[�bNSUQ�W-TUbEQ�h�M^Q�T�~�M^KNk��Nh�Q�T�TUbEQ�h�M^Q�T!m�VfY�TUvNSUM^K��4l ��vNQaSUQ�ORQ�SUTUQzh�c.�NTfc�VfM^YRK>h�c9K��EQLSUQ 8UQ�h�VfQ�kÄw��vNQtbNSUQ�WØTUbEQ�h�M^Q�T�~%M^TzKNY9V�Y�ORQ�SUv�c9SdORQ�TdVfQ�k M^K c9K Q�)0YRSdV�Y9[�TUbEQ�h�M^Q�T�m%VfY�bNSUQ�ORQ�KHV�VfvNQ�kNQ�h�j^M^KNQ�Y9[MPVfT�Y/�K bEYRb��Nj°c�VfM^YRKÄl

� � �������� ��Z����� ���& �����>(

��vNM^T�b�c9bEQ�SzbNSUY�O=M^kNQ�T�c%e-M^h�SUY9[DY��NKNk�c�VfM^YRK Y9[�M^KHVfQ�SdVfQ�e-bEYRSfc9j*bNSUQ�k�c�VfYRS¹nXbNSUQ�W SUQ�j°c�VfM^YRKNTaM^KØc>[DY=Y=kh£v�c9M^KÄl ��v�c9KN_RQ�T M^K TUbEQ�h�M^Q�T bEYRb��Nj°c�VfM^YRKNTØY�ORQ�S VfM^e-Q c9SUQÜe-Y=kNQ�j^Q�k VfvNSUY��N_Rv c TUQ,+-�NQ�KNh�Q Y9[TUvNYRSdVdnXS��NK Q�h�YRTdW=TdVfQ�e Q,+-�NM^j^M��NSUM°c��vNQ�SUQZQ�KNkNYR_RQ�KNY��NTÓTUh�c9SUh�MPVXWÙM^KNkNM^h�c�VfYRSUT�Q,+-�NM^j^M��NSfc�VfQ-kNQ�e>c9KNkNTY9[A�NM^YRe>c9TUT��HWØbNSUQ�k�c�VfYRSUT�c9KNkØVfvNQtbNSUQ�W=T � kNQ�e>c9KNk Y9[�Y/�K �NM^YRe>c9TUT�l �XK cZb�c9Sfc9e-Q�VfSUM^h�ORQ�SUTUM^YRKY9[!VfvNQ-e-Y=kNQ�ja|���Y����=n¹`aY��N_Rj°c9T£} �QZc9SUQ>c.�Nj^Q�VfY h�YRe-bNj^Q�VfQ�jPWØkNQ�SUMPORQ-VfvNQ>bEYRb��Nj°c�VfM^YRK k�W=K�c9e-M^h�T�l� jPVfvNY��N_Rv�VfvNQ�VfM^e-Q�b�c�Vfv Y9[ÆM^KHVfQ�Sfc9h�VfM^KN_tbEYRb��Nj°c�VfM^YRKNT,�Nh�YRKHORQ�SU_RQ�KNh�Q�c9KNk TdV£c.�NM^j^MPVXWZc9SUQ�KNY9V�[F�Nj^jPWh£v�c9Sfc9h�VfQ�SUM�7�Q�k c9K�c9jPW�VfM^h�c9j^jPW���Y��NS�VfvNSUQ�Q�K-�Ne-Q�SUM^h�c9j�Q��Nc9e-bNj^Q�T�c9SUQ�ORQ�SdW�M^K�[DYRSUe>c�VfMPORQ9l � j^jÄY9[VfvNQ�eQ���vNM��NMPV!h�YRKHORQ�SU_RQ�KNh�Q�VfY�c&�NKNM�+-�NQzTdVfQ�c9k�W>TdV£c�VfQ.��M^K%TdV£c9S��-h�YRKHVfSfc9TdV!VfY�VfvNQzYRT�7�M^j^j°c�VfM^YRKNTÆVXW=bNM^h�c9j0Y9[VfvNQÓTdV£c9KNk�c9SUk �Y9V���cIn��ÇYRjPVfQ�SUSfcte-Y=kNQ�j�l���vNQ�e>c9M^K SUQ�c9TUYRK [DYRSLVfvNQ�kNMPORQ�SU_RQ�KHV�k�W=K�c9e-M^h0�EQ�v�c�O=M^YRSY9[5�EY9Vfv TdW=TdVfQ�e-Ttc9SUQ%TdVfS��Nh�V��NSfc9j^jPW kNM*)0Q�SUQ�KHV�bNSUQ�WÙTUbEQ�h�M^Q�T � _RSUY/�Vfv Q,+-��c�VfM^YRKNT�M^K �EY9Vfv e-Y=kNQ�j^T| �vNM^h£vÙc9SUQ-c9k vNY=h�M^KØVfvNQ3 �Y9V���cIn��ÇYRjPVfQ�SUSfc%e-Y=kNQ�j�����V�kNQ�SUMPORQ�k [DSUYRe e-YRSUQ ��c9TUM^h-c9TUT��Ne-b�VfM^YRKNT

~Ro

Page 28: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

M^K VfvNQ>bNSUQ�TUQ�KHVtc9bNbNSUYHc9h£v4}�l �XK Y��NS�e-Y=kNQ�j]VfvNQ>bEYRb��Nj°c�VfM^YRK _RSUY/�Vfv Y9[�Q�c9h£v TUbEQ�h�M^Q�T�V��NSUKNTÓY���VVfYtv�c�ORQ�ctbEYRTUMPVfMPORQ�M^e-b�c9h�V�YRKZVfvNQ�bEYRb��Nj°c�VfM^YRK%Y9[MPVfT�bNSUQ�k�c�VfYRS5����VLKNYtbNSUQ�W�bEYRb��Nj°c�VfM^YRK%M^T�KNQ�_�nc�VfMPORQ�jPW c )0Q�h�VfQ�k �HWØVfvNQtbEYRb��Nj°c�VfM^YRKØY9[!MPVfT�bNSUQ�k�c�VfYRS�TUbEQ�h�M^Q�T�c9T�M^K VfvNQ3 �Y9V���cIn��ÇYRjPVfQ�SUSfc%e-Y=kNQ�j�l��vNM^T�bNSUYRbEQ�SdVXWØM^T�KNY9V�cZTUbEQ�h�M°c9jÆ[DQ�c�V��NSUQ�Y9[�VfvNQtb�c9Sfc9e-Q�VfSUM�7�c�VfM^YRK h£vNYRTUQ�K ����V�M^Tz_RQ�KNQ�SUM^h�[DYRS�c9j^j[DY=Y=k-h£v�c9M^KNT�l�?ÙQah�YRKM8UQ�h�V��NSUQ.�=VfvNY��N_Rv@�=Vfv�c�V�VfvNM^T�bNSUYRbEQ�SdVXW-kNY=Q�TUK � V!h�c9SUSdW-Y�ORQ�S�VfY�e-YRSUQLh�YRe-bNj^Q��[DY=Y=k��Q,�NT�lA"�Q�M^KN_th�YRK�[DSUYRKHVfQ�k��MPVfv h�YRe-bEQ�VfM^KN_�M^KNh�YRe-b�c�VfM��Nj^QaQ���bNj°c9K�c�VfYRSdWZc9bNbNSUYHc9h£vNQ�T,��[F��V��NSUQQ�e-bNM^SUM^h�c9jESUQ�TUQ�c9SUh£v M^T!KNQ�Q�kNQ�k�VfY�M^KHORQ�TdVfM^_Hc�VfQaVfvNQ�e-Q�SUMPVfT!Y9[�VfvNQ�bNSUQ�TUQ�KHVac9bNbNSUYHc9h£v c9T�h�YRe-b�c9SUQ�kVfY�VfvNQ: �Y9V���cIn��ÇYRjPVfQ�SUSfcae-Y=kNQ�j�c9KNktMPVfT]SUQ���KNQ�e-Q�KHVfT�l "A��V�KNY9V �MPVfvNTdV£c9KNkNM^KN_�Q�e-bNM^SUM^h�c9j�VfQ�TdVfM^KN_�WRQ�VVfY$�EQ��NKNkNQ�SdV£c.�9Q�K@�=�QZv�c�ORQ�TUvNY/�K Vfv�c�VÓVfvNQZe-M^h�SUY9[DY��NKNk�c�VfM^YRK T��N_R_RQ�TdVfQ�k2vNQ�SUQZh�c9KNKNY9VtTUQ�SdORQc9T-c VfvNQ�YRSUQ�VfM^h�c9j���c9TUM^T�[DYRS�_RQ�KNQ�Sfc�VfM^KN_ØVfvNQ; �Y9V���cIn��ÇYRjPVfQ�SUSfc bEYRb��Nj°c�VfM^YRK _RSUY/�VfvÜ[F�NKNh�VfM^YRKNT�l ��VSUQ�e>c9M^KNT�c9K YRbEQ�K;+-�NQ�TdVfM^YRK;�vNQ�VfvNQ�SLVfvNQ�SUQ�M^TLc�Vac9j^j�cte-Y=kNQ�jÄh�c9b�c.�Nj^Q�VfY-TUQ�SdORQÓc9Tac�VfvNQ�YRSUQ�VfM^h�c9j�NKNkNQ�SUbNM^KNKNM^KN_tY9[*VfvNQ�TUQ�[F�NKNh�VfM^YRKNT�l

� T]VfvNQ�bNSUQ�h�Q�kNM^KN_�c9K�c9jPW=TUM^T]v�c9TÇkNQ�e-e-YRKNTdVfSfc�VfQ�ktY��NS]e-Y=kNQ�j^M^KN_zY9[0Q�h�YRTdW=TdVfQ�e VfSfc9KNTfc9h�VfM^YRKNTc9KNk%Q,+-�NM^j^M��NSUM��Ne M^TA+-�NMPVfQaM^KHORYRjPORQ�kÄl "A��V!MPV�M^T�TUM^e-bNj^QLQ�KNY��N_Rv@��YRK>VfvNQaY9VfvNQ�S!v�c9KNk@�=VfY�TUQ�SdORQ�c9T�c[DSfc9e-Q��YRS���[DYRS*V£c9h��j^M^KN_�c:�M^kNQ�Sfc9KN_RQ!Y9[4SUQ�j^Q�O9c9KHVÆM^TUT��NQ�T�l � e-YRKN_zY9VfvNQ�S*VfvNM^KN_RT,�RkNQ�O=M°c�VfM^YRKNT*[DSUYRe�NKNM^kNM^SUQ�h�VfM^YRK�c9jE[DY=Y=k�h£v�c9M^KNTLh�Y��Nj^k��EQ�TdV��NkNM^Q�k c9KNk c9jPVfQ�SUK�c�VfMPORQ�bNSUYRbEQ�SdVXW�SUM^_RvHVfT�Y9[VfvNQ�SUQ�TUY��NSUh�Qe>c�W6�EQ�c9TUT��Ne-Q�k�M^KNh�j��NkNM^KN_�TUh£vNQ�e-Q�T��vNQ�SUQ�c9j^jETUbEQ�h�M^Q�T�Y/�K�TUv�c9SUQ�T�Y9[�VfvNQ�SUQ�TUY��NSUh�Q9l ��vNQ�e-YRTdVbNSUYRe-M^TUM^KN_�Q��=VfQ�KNTUM^YRK�M^T*bNSUY���c.�NjPWzVfYLj^M^K���cÓ|DTdV£c9KNk�c9SUk�bEQ�Sd[DQ�h�VfjPW�h�YRe-bEQ�VfMPVfMPORQ�}0Q�h�YRKNYRe�W!�MPVfv�VfvNQQ�h�YRTdW=TdVfQ�e VfYzc9K�c9jPW<7�QÇVfvNQ�M^e-b�c9h�VfT*Y9[�v-�Ne>c9KÓc9h�VfMPO=MPVfM^Q�T�YRK�VfvNQ�Q�h�YRTdW=TdVfQ�e c9KNk�MPVfT*SUQ�bEQ�SUh,�NTUTUM^YRKNTYRKZVfvNQ�Q�h�YRKNYRe�WRl

� ����!���������(

�!c9KHVfSUQ�j^j ��lL\El�c9KNk �al:��YRTUKNQ�S |�~9qRq��I} �9yzK VfvNQ k�W=K�c9e-M^h�TZY9[ÓbNSUQ�k�c�VfYRS¹nXbNSUQ�W e-Y=kNQ�j^T��MPVfvVfvNQ�"�Q�kNkNM^KN_9VfYRK=n¹`aQ � KN_RQ�j^M^T][F�NKNh�VfM^YRK�c9j4SUQ�TUbEYRKNTUQ.��� � � � 1P��4 ��A�� ��>&@ � �N��> � ����4 1P��4�5�� � �{��1 � �3�"4 � ����> �0� 1*� ����� �E~9qRrInd~R~R~=l

��j°c9S�� �al�?Òl!|¹��{Hp9rH} � � ��>&@ � �N��> � ����4 �K�0��� � � 1 � � � ���_>&@ � � �"> � �N��4#�N��1P� 9�� � � 1�> ��AN��� 1 � � � � 4 ���� � � � � � � ����?�M^j^Q�W���>LQ� ��YRS��4l

��SUY=h�9Q�S'��l*`�l*c9KNk���l �*TUh£vNM^SUv�c9SdV%|¹��{R{H~R} �*g]h�YRTdW=TdVfQ�e-T,�Q��=VfQ�SUK�c9j^MPVfM^Q�T�c9KNkÙQ�h�YRKNYRe-M^Q�T,� 1 ��� <��� 1S� � 1�> ��4 ��1 �� F� � � � � � � � � 1 � � � ��� �@�EoRo=��ndo9rHp=l

`aQ,�NSUQ,� u l�|¹��{Ho9{H} � � @ �7�[� 5 ��A{� ��4 � � ��?�M^j^Q�W���>LQ� ��YRS��4l

g]M^h£vNKNQ�SA��l�c9KNk���l<1*Q�VfvNM^_Z|�~9qRqRmH} �-��vNQzM^e-b�c9h�VÇY9[�TUh�c9SUh�MPVXW>c9KNkZc.���NKNk�c9KNh�QaM^K-[DY=Y=k-h£v�c9M^KNT�YRKTUbEQ�h�M^Q�T�bEYRb��Nj°c�VfM^YRK%k�W=K�c9e-M^h�T,��� ��> � � ��4 F� � � � � � ���T�D��� 4 � 1 9 ��[DYRSdVfvNh�YRe-M^KN_Nl

~9r

Page 29: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

M^KNKNY.)Ø`�l4c9KNk ��l��*TUh£vNM^SUv�c9SdVÓ|�~9qRqRmH} ��iac9SdORQ�TdVfM^KN_tM^K c9K Q�M^_RvHVdnXTUbEQ�h�M^Q�T�Q�h�YRTdW=TdVfQ�e;� � � � � 1P��4 ��A 1 ������ 1S� � 1�> ��4 � � 1 � � � ��� ��1 � � ��1P� 9�� � � 1�> �=[DYRSdVfvNh�YRe-M^KN_Nliac9KNKNYRK "al�|¹��{Hp9rH} ��� c9SU_RM^K�c9jLbNSUY=k��Nh�V bNSUM^h�M^KN_ M^K VfvNQ Q�h�YRTdW=TdVfQ�e;� � � � � 1P��4 ��A � @ �7�[��� > � ����4

. �0� 4 ��9 5�� � �E~Ro9mInd~9rHp=liLM^SUTUvNj^Q�MP[DQ�S ��lL|¹��{HpRpR} ��g]h�YRKNYRe-M^h�T�[DSUYRe c �NM^YRj^YR_RM^h�c9jÇO=M^Q��bEYRM^KHVI��� � � � 1P��4 ��A �0� � ��1 � � � <

1 � � � ��� ��� ����ndoR~=l

!��c9KN_ ��l9c9KNkÓg�l "�Q�SUQ�VUV£cÓ|¹��{R{RsH} � u j^Y���c9j�+-��c9j^MPV£c�VfMPORQ�c9K�c9jPW=TUM^T�Y9[�cLSfc�VfM^Y�nXkNQ�bEQ�KNkNQ�KHVbNSUQ�k�c�VfYRS¹nbNSUQ�WZTdW=TdVfQ�e;� � � � � 1P��4 ��A � ��>&@ � �N��> � ����4". �0� 4 ��9 5 � � ��mRsR{InXyHqRr�l

�M^e>ct\El� ]l4c9KNk4 ]l � l4`aM�� |¹��{R{RqH} � "�Q�v�c�O=M^YRSfc9j�kNQ�h�M^TUM^YRKNT�e>c9kNQ��NKNkNQ�S�VfvNQ�SUM^T��%Y9[ÆbNSUQ�k�c�VfM^YRKÄwc�SUQ�O=M^Q� c9KNk bNSUYRTUbEQ�h�V��NT,���#��1P� �� ��1 � � � � 1P��4 ��A�� �2� 4 ��9 5 �� �4r���{In¹r9yHq�l

�Y9V���c � l���l*|¹��{H~RoR} � 4 � � � 1�>� ��A ��@ 5�� � ����4 �K�0� 4 ��9 5 ��?�M^j^j^M°c9e-T=�NKNk�?�M^j���M^KNT,��"!c9jPVfM^e-YRSUQ9l

� c�W ��l � l|¹��{Hp9mH} �� > � �K� 4 � >/5_��1 � � � �O�"4 ���J� >/5 � 1�� �D��� 4 � � � �h5��h> � � ����� YRKNYR_RSfc9bNvNTLM^K41*YRb��Nj°cInVfM^YRK�"�M^YRj^YR_9W3� �� 1]SUM^KNh�Q�VfYRK JLKNMPORQ�SUTUMPVXW�1]SUQ�TUT,��1]SUM^KNh�Q�VfYRKÄl

� c�W ��l � l�|¹��{Rs��I} � � @ �7�[��� > � ����4 � � � 4 ��9 5 � ��� 1 � � �"4 � �N��1 � ��3�"4 � ����> �0� 1*����~�KNk Q�kNKÄl3"�j°c9h� �Q�j^j��yL�=[DYRSUkÄl�;�NSUSfc�W ��l4`�l*|¹��{R{RmH} � � ��>&@ � �N��> � ����4 �K�0� 4 ��9 5 �4~�KNk�Q�kNKÄl!\=bNSUM^KN_RQ�S,� "�Q�SUj^M^KÄl1*Q�VfvNM^_ ��l=|�~9qRqRmH} � � _RSUM^h,�NjPV��NSUQ.��bEQ�TdVfM^h�M^kNQ�T*c9KNk�VfvNQÇQ�h�YRTdW=TdVfQ�e;� 9��� ��� 4�> � � ��4 � � 1 � � � ������[DYRSdVfv=n

h�YRe-M^KN_Nl

1*Q�VfvNM^_ ��lNc9KNk ��l��*TUh£vNM^SUv�c9SdV�|�~9qRq��I} � � M^h�SUY9[DY��NKNk�c�VfM^YRKNT�Y9[*bEYRb��Nj°c�VfM^YRK>k�W=K�c9e-M^h�T,��� � � � 1P��4 ��A. �0��� � � 1 � � � ����� �@�4~Rp�nXyH{�l

��YRTUQ�K u lÇ|¹��{Rs9y�} � ��v�c9Sfc9h�VfQ�SUM�7�M^KN_�h�YRKNkNMPVfM^YRKNT�[DYRS�_RQ�KNQ�Sfc9j^M�7�Q�k �ÇQ�SUv-�Nj^TdV�j^YR_RM^TdVfM^h�_RSUY/�VfvÙY9[�c�NM^YRj^YR_RM^h�c9j4bEYRb��Nj°c�VfM^YRK@��.F� 4&4 � > � 1 ��A � ��>&@ � �N��> � ����4 . �0� 4 ��9 5 � � �4{RrRmIn¹{RrHo=l

�*TUh£vNM^SUv�c9SdV ��l�|�~9qRqRqH} � u Q�KNQ�Sfc9jÄQ,+-�NM^j^M��NSUM��Ne Y9[c9K�Q�h�YRTdW=TdVfQ�e;� � � � � 1P��4 ��A � @ �7�[��� > � ����4 . �0� 4 ��9 5��� �@�Ä��mIn¹mH~=l

�*TUh£vNM^SUv�c9SdV ��l�|�~9qRqH~R} � ��Q�TUY��NSUh�Q�h�YRe-bEQ�VfMPVfM^YRK%c9e-YRKN_ÓbNj°c9KHVfT�w[DSUYRe YRb�VfM^e-M�7�M^KN_�VfY�h�YRe-e0�NKNMPVXWTdVfS��Nh�V��NSUQ.� � � 4 ��9� ����4 �T�D��� 4&4 � 1 9 ) � � �Ä��{���nd~=�I~=l

�ÇYRjPVfQ�SUSfc0�Ól|¹��{H~9rH} ����c9SUM°c.7�M^YRKNM^Q&x ��VUV���c.7�M^YRKNM�kNQ�j�K-�Ne-Q�SUY>k � M^KNkNMPO=M^k��NMÄM^K TUbEQ�h�M^QÓc9KNM^e>c9j^M0h�YRK=nO=MPORQ�KHVfM�� � � � � ��� � � � � 1 � ��� � �@�Äm���n£�R��m | ��c9SUM°c�VfM^YRKNTLc9KNk j��Nh�V���c�VfM^YRKNTLY9[�c�>:�Ne0�EQ�SzY9[�XKNkNMPO=M^k���c9j^TÆM^K � KNM^e>c9j�\=bEQ�h�M^Q�T= �MPO=M^KN_��*YR_RQ�VfvNQ�S,�-�*Sfc9KNTUj°c�VfM^YRK �XK���v�c9bNe>c9K ��l >�lE|¹��{Rm��I} � 1 � �N��4 � � 4 ��9 5 ��yHqR{InXyRyHs���� h u SfcI�iLM^j^j���>LQ� ��YRS��4l

~Rp

Page 30: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

� � ������Z��� ��� ����t��9(

����� ��� ��� � ��� ���"!$#&%�#'�"(*) %���vNQ' �c9_RSfc9KN_RQ�c9K�c9TUTUY=h�M°c�VfQ�kZVfYÓVfvNQ�YRb�VfM^e-M�7�c�VfM^YRK-bNSUY��Nj^Q�e |Dy�}�[DYRSEHG <JIDBDBDBKI�7 M^T�_RMPORQ�K��HW

�O ^QSOUTSV�I�Z[O I��!O I�� � O`#GAc O ^QSOUTSV�I�Z[O` ��!O*^ �!O Z[O : �!OUTSV(QSOUTSV�` �� � O�^aZ[O : ��O QSOUTSV `

c9KNk�VfvNQ�h�YRSUSUQ�TUbEYRKNkNM^KN_3 !�NvNK=n ���Nh�9Q�SLh�YRKNkNMPVfM^YRKNT�c9SUQ

� Ot��� G c Ot :�!O �!OUTSVH:� � O ��O8/ m I QSOUTSV � Ot��� G m I |�~9rRcH}� Oz� G c Oz ��!O �!O �� � O�/ m I Z[O � Oz� G m I |�~9r.�4}� O � G �!O Z[O : �!OUTSV(QSOUTSV � m I �!O � O � G m I |�~9r9h�}� O ��� G Z[O : ��OUQSOUTSV � m I � � O � O ��� G m B |�~9r9k4}

|8cH} \<�NbNbEYRTUQ �!OUTSVsG �!O#G m l���vNQ�KYQSOUTSV u m �ÄTUM^KNh�QRc Ot u m Q�O9c9j���c�VfQ�k c�V9QSOUTSV&G m l�` �NQ�VfY|8mH}�QSOUTSV u m M^e-bNj^M^Q�TFZ[O u m l���vNQ�SUQ�[DYRSUQ_: � c Ot �c Oz � G ��OÆ[DYRj^j^Y/�T�[DSUYRe |�~9rRcH}Lc9KNk2|�~9r.�4}�vNM^h£v M^T�Tfc�VfM^T2��Q�k M*) QSOUTSVXG Q �OUTSV l

|F�4} \<�NbNbEYRTUQ�KNQ��=V �!O u m c9KNk �!OUTSV G m l � TaM^K bEYRM^KHVÓ|8cH}�c.�EY�ORQ.� QSOUTSV u m c9KNk Z[O u m lA?�MPVfv�!O u m c9KNk��!OUTSVNG m |�~R}'�EQ�h�YRe-Q�T �!O Z[Ov: �!OUTSV(QSOUTSVNG �!O Z[O u m l iLQ�KNh�Q �!O{G m l ��vNQM^e-bNj^M^h�c�VfM^YRKRQ��OUTSV G=Q��OUTSV [DYRj^j^Y/�T�c9T�M^K�bEYRM^KHV�|8cH}�l

|Dh�} \<�NbNbEYRTUQ �!O u m � �!OUTSV u m c9KNk��SOUTSV � G �!OUTSV�� �!O w ��O�l���vNQ�K%[DYRS�c9j^j �QSOUTSV u m MPV�M^TÇVfS��NQLVfv�c�V�SOUTSV �QSOUTSV w ��O �QSOUTSV�l�iLQ�KNh�Q�c9j^j5^QSOUTSV�I�Z[O`!Tfc�VfM^Td[ÂW=M^KN_ |8mH}�M^e-bNjPWNZ[O u �SOUTSV(QSOUTSV�c9KNkZVfvNQ�SUQ�[DYRSUQ�!O1G m l � _Hc9M^K@�6: � c Ot �c Oz � G ��O�[DYRj^j^Y/�T�[DSUYRe |�~9rRcH}�c9KNk |�~9r.�4}�W=M^Q�j^kNM^KN_ Q��OUTSV G=Q��OUTSV l

|Dk4} ��[ �!O u m � �!OUTSV u m c9KNk �SOUTSV�G ��O �EY9Vfv h�YRKNTdVfSfc9M^KHVfT�|�~R}�c9KNk |8mH}�h�YRM^KNh�M^kNQ.�Ec9KNk VfvNQ�SUQ�[DYRSUQQ��OUTSV G=Q��OUTSV l|DQ�} \<�NbNbEYRTUQ �!O u m � �!OUTSV u m c9KNk �SOUTSV u ��O�l ��vNQ�K �SOUTSV �QSOUTSV u ��O �QSOUTSV�[DYRS�c9j^j �QSOUTSV u m l

iLQ�KNh�Q-c9j^j�^QSOUTSV�I�Z[O`aTfc�VfM^Td[ÂW=M^KN_ |�~R}aM^e-bNjPW Z[O u ��OUQSOUTSV�c9KNkØVfvNQ�SUQ�[DYRSUQ�� � G m l&��vNQ�SUQ�[DYRSUQ: � c Ot �c Oz � G �SOUTSV�[DYRj^j^Y/�T�[DSUYRe |�~9rRcH}!c9KNkÙ|�~9r.�4}A�vNM^h£v M^T�Tfc�VfM^T2��Q�k M*) QSOUTSVXG Q� OUTSV l��

����� ��������� ��� ���"!$#&%�#'�"( ��% �XKtVfvNQ�e>c9S��9Q�V][DYRSVfvNQ�SUQ�TUY��NSUh�Q ^aEHG m `Æc9KtQ,+-�NM^j^M��NSUM��NeÒQ���M^TdVfT[DYRS�c9KHW �DV u m l�iLQ�KNh�Q �DV!h�c9K4�EQ!����Q�k c.��VfYRKNYRe-Y��NTUjPWRl �YRS!VfvNQ�e>c9S��9Q�VfTFEfG�<JIDBDBDBKI�7 : <�VfvNQQ,+-��c�VfM^YRKNT9MPO � O ^ ��Oa`FGWMPO g V � O ^ ��O g V�`�YRS9MPO ��O�� OUTSV ^ ��Oa`FGWMPO g V � O ^ ��O g V `�[DYRS9E GL<JIDBDBDB�I�7>:A<�c9SUQT�� �-h�M^Q�KHV�VfY�bNSUQ�ORQ�KHV�c9KØQ���h�Q�TUT�T��NbNbNjPW YRKØe>c9S��9Q�V EUl�` �NQÓVfY � TUT��Ne-b�VfM^YRK ��MPVzM^TzbEYRTUTUM��Nj^Q�VfYQ�TdV£c.�Nj^M^TUvZVfvNQ�TUQ�Q,+-��c�VfM^YRKNT5�HW�c�T��NMPV£c.�Nj^Q�h£vNYRM^h�Q�Y9[ ��O g V�[DYRS�c9KHWZ_RMPORQ�K ��O u m l

?ÙQ�kNQ�KNY9VfQ��HW �� O VfvNQ�M^KHORQ�SUTUQ�[F�NKNh�VfM^YRKZVfY � O c9KNk TUYRjPORQz[DYRS ��O g V�w��O g V#G �� O�� ��O MPOMPO g V � OUTSV ^ ��Oa`�� EHG�<JIDBDBDB�I�7 : <JB |�~RpR}

~9s

Page 31: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

\=M^KNh�Q �DV�h�c9K0�EQ�h£vNY=YRTUQ�KÓ[DSUQ�Q�jPW�VfvNQ�Q,+-��c�VfM^YRKNT�|�~RpR} �NKNM�+-�NQ�jPW�kNQ�VfQ�SUe-M^KNQ�c9j^j ��O�[DYRSvEHG]@�IDBDBDBKI�7,:<Rl � YRSUQ�Y�ORQ�S,�tYRK VfvNQ e>c9S��9Q�VØ[DYRS VfvNQÜSUQ�TUY��NSUh�Qd^aE,G m ` c �NKNM�+-�NQ �EY��NKNkNQ�kÒQ,+-�NM^j^M��NSUM��NebNSUM^h�Q1���9 � m c9j*!c�W=T Q���M^TdV�l ��[ÓVfvNQÙb�c9Sfc9e-Q�VfQ�S � ; M^T h£vNYRTUQ�KÒc9T kNQ�VfQ�SUe-M^KNQ�kAM^K |�~RpR}%VfvNQ�KVfvNQ�SUQ M^T����V � m T��Nh£v Vfv�c�V M V �DV�� 9 ^.���9 ` G M ;�� V ^.���V `3�EQ�h�c.�NTUQ VfvNQ kNQ���KNMPVfM^YRK Y9[ � ;ZM^e-bNj^M^Q�TM ;�� V ^ � ;�` �jM V��DV � 9 ^.��9�`�[DYRS>c9j^j ��9 � m c9KNk �EQ�h�c.�NTUQ � TUT��Ne-b�VfM^YRKA� TUQ�h,�NSUQ�T>Vfv�c�V>[DYRS>c9KHW� 50p m I�M V��DV�� 9 ^ �DV ` l YRKNQ�h�c9K(��KNk0�6V � m T��Nh£v-Vfv�c�V#M ;�� V ^.�6V�`5G � l���vNQLTfc9e-Q�c9SU_��Ne-Q�KHV�c9bNbNj^M^Q�TVfY-c9j^jÄT����NTUQ,+-�NQ�KHVze>c9S��9Q�VfTFEHG]@�IDBDBDB�I�7 : <Rl �

����� ���,��� � ��� ���"!$#&%�#'�"( �!%���vNQ���SUTdVdnXYRSUkNQ�S!h�YRKNkNMPVfM^YRKNT�Y9[�VfvNQzYRb�VfM^e-M�7�c�VfM^YRKtbNSUY��Nj^Q�e |Dy�}c9SUQzQ�MPVfvNQ�S9:&c Ot �c Oz G ��O��!Z[O1G ��OUQSOUTSV�YRS9:&c Ot �c Oz G �SOUTSV �!Z[O1G �SOUTSV(QSOUTSV=�vNM^h£vZM^e-bNjPWtkNQ�e>c9KNkc9KNk T��NbNbNjPW%[F�NKNh�VfM^YRKNT

QSOUTSV#G � OUTSV ^ ��Oa`PI�Z[O1G � O ^ ��Oa` YRS QSOUTSV#G �� OUTSV ^.�SOUTSV�`PI�Z[O6G �� O ^.�SOUTSV�`PB |�~9sH}

�Q�V&�NT'��SUTdV�h�YRKNTUM^kNQ�S�VfvNQ>h�c9TUQ>Y9[�c9K c.���NKNk�c9KHV�SUQ�TUY��NSUh�Q9l �DV�h�c9K �EQ-h£vNY=YRTUQ�KÙ[DSUQ�Q�jPW c9KNk VfvNQQ,+-�NM^j^M��NSUM��NeÒh�YRKNkNMPVfM^YRKNTL|�o �4}h�c9K3�EQ�TUYRjPORQ�k3�EY9VUVfYRe �Nb>c9KNk�VfvNQ�Q,+-�NM^j^M��NSfc�VfM^KN_zb�c9Sfc9e-Q�VfQ�SUT]v�c�ORQVfvNQ�[F�NKNh�VfM^YRK�c9j0[DYRSUe

��O6G , O ^aM V�IDBDBDB�I�MPO ` EHG]@�IDBDBDB�I�7�I |�~9{H}

�vNM^h£v M^KZV��NSUK�W=M^Q�j^kNT�Q,+-�NM^j^M��NSUM��Ne kNQ�e>c9KNkNTLc9KNk T��NbNbNj^M^Q�T

Q�9 G � 9 ^ �DV `1I�Z�V5G � V ^ �DV�` |8mRqRcH}QSOUTSVjG � OUTSV � , O ^aM V�IDBDBDBKI�MPOa` � I�Z[O1G � O � , O ^aM V�IDBDBDBKI�MPOa` � EHGd@�IDBDBDBKI�7�B |8mRq.�4}

>LY/ �QaV��NSUK>VfYÓc9K%Q�h�YRTdW=TdVfQ�e �MPVfv%c�TUh�c9SUh�QzSUQ�TUY��NSUh�Q9l ��vNQzQ,+-�NM^j^M��NSUM��Ne h�YRKNkNMPVfM^YRKNTa|�o9cH} �MPVfvQ,+-��c9j^MPVXWÓc9KNk |�o �4}*h�c9K(�EQ!TUYRjPORQ�k(�EY9VUVfYRe �Nb �MPVfvÓVfvNQ!h�YRKNTUQ,+-�NQ�KNh�QLVfv�c�VÆVfvNQ!Q,+-�NM^j^M��NSUM��Ne�VfQ�SUe-TY9[*VfSfc9kNQ�v�c�ORQ�VfvNQ�[F�NKNh�VfM^YRK�c9jE[DYRSUe

�SOUTSV#G�� OUTSV ^aM V�IDBDBDB�I�MPOa` EHG�<JIDBDBDB�I�7�B |8m��I}

�XKNTUQ�SdVfM^KN_�VfvNQLQ,+-�NM^j^M��NSUM��NeÒVfQ�SUe-TÇY9[0VfSfc9kNQ�|8m��I}ÆM^KHVfY�VfvNQLkNQ�e>c9KNk>c9KNk-T��NbNbNjPW�[F�NKNh�VfM^YRKNTa|�~9sH}��QY���V£c9M^K

QSOUTSVXG �� OUTSV � � OUTSV ^aM V�IDBDBDBKI�MPOa` � c9KNk Z[O1G �� O � � OUTSV ^aM V�IDBDBDBKI�MPOa` � B |8mH~R}

M^K�c9j^jPW�bNj��N_R_RM^KN_-|8mRqRcH}�n�|8mRq.�4}c9KNk |8mH~R} ��SUQ�TUbEQ�h�VfMPORQ�jPW���M^KHVfY�VfvNQLKNQ�V=�NM^YRe>c9TUTÆ[F�NKNh�VfM^YRK |¹�I} �vNM^h£vM^KZV��NSUK M^T�M^KNTUQ�SdVfQ�k M^KHVfY |8{H}�Q�TdV£c.�Nj^M^TUvNQ�T�bNSUYRbEYRTUMPVfM^YRKZyNl �

~9{

Page 32: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

� � ������Z����� � ��� � ����& � ����������� (�*�������!(

"�Q�[DYRSUQ!�Q�V��NSUK�VfY�VfvNQ�kNM*)0Q�SUQ�KHVfM°c�VfM^YRKZY9[*VfvNQ�Q,+-�NM^j^M��NSUM��Ne Q,+-��c�VfM^YRKNTnZ�9 G M V(Q�9�I |8mRmRcH}M V(Z�VjG M ;�Q6V�I |8mRm.�4}M ;�Z�; G M���Q�;�I |8mRm9h�}MPV M^T h�YRKHORQ�KNM^Q�KHV VfY kNQ���KNQ#VfvNQ#[DYRj^j^Y/�M^KN_ VfQ�SUe-T �NTUQ�k �EQ�j^Y/ VfY c�ORYRM^k h�j���VUVfQ�S�w� OUTSV#G �� OUTSV �SOUTSV

�� OUTSV w m ����O6G �� O �SOUTSV�� O / m � � O% t G c Ot QSOUTSVc O u m � � O% z G c Oz Z[Oc O w m l

`aM*)0Q�SUQ�KHVfM°c�VfM^YRKZY9[�|8mRmRcH}Çnz|8mRm9h�}�W=M^Q�j^kNT�w � ��nZ�9 G �M V � �Q�9�I |8m9yHcH}

�M V � �Z�VjG �M ; � �Q6V�I |8m9y��4}�M ; � �Z�; G �M�� � �Q�;�B |8m9yRh�}

>LQ��=V5�Q�kNM*)0Q�SUQ�KHVfM°c�VfQ9QSOUTSV#G �� OUTSV ^ �SOUTSV�`�c9KNk Z[O6G �� O ^.�SOUTSV�`�VfY-Y���V£c9M^KÄw�QSOUTSV#G � OUTSV ��SOUTSV c9KNk �Z[O1G���O ��SOUTSV�B |8mHoR}

��VLM^T�Q�c9TdW%VfYtTUvNY/�Vfv�c�V�|8mHoR}�[DYRS�EHG�<�c9KNk |8m9yHcH}�SUQ�T��NjPVLM^KÄw���9�G �nZ�9

� 9 : �M V� 9 B |8mRrH}

>LQ��=VI���Q�h�YRe0�NM^KNQ-|8m9y��4} ��|8mHoR}�[DYRS�EHG�<JI�@Óc9KNk |8mRrH}�VfYtkNQ�SUMPORQ9w��6V#G �oV

� V � 9 �nZ�9 � � 9X:��oV� V � 9 �M Vf: �M ;� V B |8mHpR}

?ÙQ�KNY/�M^KNTUQ�SdVÓ|8mHoR}Ç[DYRS�EHG]@�I ��h�YRe0�NM^KNQ�k��MPVfv ��6V�[DSUYRe |8mHpR}�M^KHVfY |8m9yRh�}�VfY-_RQ�V�w

���;�G � ;�oV� ; � V � 9 �nZ�9 � � ;H^ � 9#:�oV `� ; � V � 9 �M V � � VH:� ;� ; � V �M ;X: �M��� ; B |8mRsH}

��vNQ�KNQ��=VaTdVfQ�b M^T!VfY-M^KNTUQ�SdV�|8mRrH}Çnz|8mRsH}�M^KHVfY |8mHoR}�VfYtkNQ�SUMPORQ9w

�Q�9 G �nZ�9#: �M V�I |8mR{RcH}�Q6VrG �oV

� 9 �nZ�9 � � 9X:��oV� 9 �M Vf: �M ;�I |8mR{.�4}

�Q�; G � ;��oV� V � 9 �nZ�9 � � ;v^ � 9X:�oV `� V � 9 �M V � � Vf:� ;� V �M ;X: �M���I |8mR{9h�}

�Z�VjG �oV� 9 �nZ�9#: �oV� 9 �M V�I |8mR{9k4}

�Z�; G � ;��oV� V � 9 �nZ�9 � � ;v^ � 9X:�oV `� V � 9 �M VH: � ;� V �M ;DI |8mR{9Q�}

�Z�� G � ��� ;��oV� ; � V � 9 �nZ�9 � � ��� ;H^ � 9X:��oV `� ; � V � 9 �M V � � �H^ � VH:� ;�`� ; � V �M ;X: � �� ; �M���B |8mR{�[£}

� � Áµz¿�·�«£¬�»¼­�² ² ­£¿�¶0¿0©]ª�©dµI­�¬�©]¾�± ��� ~�� �� ¬�·I©]½�«�¨�È�´ µ�«�²R¨�©d²³«£¬�´ Ã�©]¸�·�«�µIÈ�©U¶0­�»N«�² ²�ã«�¨�´³«�¾I² ©U¶ � À

mRq

Page 33: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

?ÙQ�KNY/�h�YRe-bNj^Q�VfQaVfvNQ�h�YRe-b�c9Sfc�VfMPORQzTdV£c�VfM^h�T%�HW%kNM*)0Q�SUQ�KHVfM°c�VfM^KN_ b O0GAc O ^QSOUTSV�I�Z[Oa`�[DYRSCEHG�<JI�@�I ��w�b VrG �

V% t �Q�9 � � V% z �Z�V�I |DyHqRcH}�b ; G �

;% t �Q6V � � ;% z �Z�;DI |DyHq.�4}�b � G �

�% t �Q�; � � �% z �Z��DI |DyHq9h�}

c9KNk�VfvNQ�K bNj��N_R_RM^KN_�|8mR{RcH}Çnz|8mR{�[�}�M^KHVfY |DyHqRcH}Çnz|DyHq9h�}�Q�TdV£c.�Nj^M^TUvNQ�T�w

�b VrG � V% t � 9 � � V% z �oV� 9 �nZ�9#: � V% t � 9 � � V% z �oV

� 9 �M V�I |DyN��cH}

�b ; G � ;% t � V �oV � � ;% z � ;��oV� V � 9 �nZ�9 �d^ � 9X:�oV ` � ;% t � V � � ;% z � ;� V � 9 �M Vf: � ;% t � V � � ;% z � ;� V �M ;DI |DyN�I�4}

�b � G � ;��oV � �% t � ; � � �% z � �� ; � V � 9 �nZ�9 � � ;�^ � 9X:� ;�` � �% t � ; � � �% z � �� ; � V � 9 �M V �d^ � Vf:� ;�` � �% t � ; � � �% z � �� ; � V �M ;

: � �% t � ; � � �% z � �� ; �M���B |DyN��h�}

m��

Page 34: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

CESifo Working Paper Series(for full list see www.cesifo.de)

________________________________________________________________________

884 Eytan Sheshinski, Note on the Optimum Pricing of Annuities, March 2003

885 Paul De Grauwe and Magdalena Polan, Globalisation and Social Spending, March 2003

886 F. van der Ploeg, Do Social Policies Harm Employment and Growth?, March 2003

887 Mirjam van Praag, Initial Capital Constraints Hinder Entrepreneurial VenturePerformance: An empirical analysis, March 2003

888 Bernard Steunenberg, Coordinating Sectoral Policymaking: Searching forCountervailing Mechanisms in the EU Legislative Process, March 2003

889 Eytan Sheshinski, Optimum Delayed Retirement Credit, March 2003

890 Frederick van der Ploeg, Rolling Back the Public Sector – Differential effects onemployment, investment and growth, March 2003

891 Paul De Grauwe and Marc-Alexandre Sénégas, Monetary Policy in EMU when theTransmission is Asymmetric and Uncertain, March 2003

892 Steffen Huck and Kai A. Konrad, Strategic Trade Policy and the Home Bias in FirmOwnership Structure, March 2003

893 Harry Flam, Turkey and the EU: Politics and Economics of Accession, March 2003

894 Mathias Hoffmann and Ronald MacDonald, A Re-examination of the Link betweenReal Exchange Rates and Real Interest Rate Differentials, March 2003

895 Badi H. Baltagi, Espen Bratberg, and Tor Helge Holmås, A Panel Data Study ofPhysicians’ Labor Supply: The Case of Norway, March 2003

896 Dennis C. Mueller, Rights and Citizenship in the European Union, March 2003

897 Jeremy Edwards, Gains from Trade in Tax Revenue and the Efficiency Case for TradeTaxes, March 2003

898 Rainer Fehn and Thomas Fuchs, Capital Market Institutions and Venture Capital: DoThey Affect Unemployment and Labour Demand?, March 2003

899 Ronald MacDonald and Cezary Wójcik, Catching Up: The Role of Demand, Supply andRegulated Price Effects on the Real Exchange Rates of Four Accession Countries,March 2003

Page 35: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

900 R. Selten, M. Schreckenberg, T. Pitz, T. Chmura, and S. Kube, Experiments andSimulations on Day-to-Day Route Choice-Behaviour, April 2003

901 Stergios Skaperdas, Restraining the Genuine Homo Economicus: Why the EconomyCannot be Divorced from its Governance, April 2003

902 Yin-Wong Cheung, Menzie D. Chinn, and Antonio Garcia Pascual, What Do We Knowabout Recent Exchange Rate Models? In-Sample Fit and Out-of-Sample PerformanceEvaluated, April 2003

903 Mika Widgrén, Enlargements and the Principles of Designing EU – Decision-MakingProcedures, April 2003

904 Phornchanok Cumperayot, Dusting off the Perception of Risk and Returns in FOREXMarkets, April 2003

905 Kai A Konrad, Inverse Campaigning, April 2003

906 Lars P. Feld and Stefan Voigt, Economic Growth and Judicial Independence: CrossCountry Evidence Using a New Set of Indicators, April 2003

907 Giuseppe Bertola and Pietro Garibaldi, The Structure and History of ItalianUnemployment, April 2003

908 Robert A.J. Dur and Otto H. Swank, Producing and Manipulating Information, April2003

909 Christian Gollier, Collective Risk-Taking Decisions with Heterogeneous Beliefs, April2003

910 Alexander F Wagner, Mathias Dufour, and Friedrich Schneider, Satisfaction notGuaranteed – Institutions and Satisfaction with Democracy in Western Europe, April2003

911 Ngo Van Long, Raymond Riezman, and Antoine Soubeyran, Trade, Wage Gaps, andSpecific Human Capital Accumulation, April 2003

912 Andrea Goldstein, Privatization in Italy 1993-2002: Goals, Institutions, Outcomes, andOutstanding Issues, April 2003

913 Rajshri Jayaraman and Mandar Oak, The Signaling Role of Municipal Currencies inLocal Development, April 2003

914 Volker Grossmann, Managerial Job Assignment and Imperfect Competition inAsymmetric Equilibrium, April 2003

915 Christian Gollier and Richard Zeckhauser, Collective Investment Decision Making withHeterogeneous Time Preferences, April 2003

916 Thomas Moutos and William Scarth, Some Macroeconomic Consequences of BasicIncome and Employment Subsidies, April 2003

Page 36: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

917 Jan C. van Ours, Has the Dutch Miracle Come to an End?, April 2003

918 Bertil Holmlund, The Rise and Fall of Swedish Unemployment, April 2003

919 Bernd Huber and Marco Runkel, Optimal Design of Intergovernmental Grants underAsymmetric Information, April 2003

920 Klaus Wälde, Endogenous Business Cycles and Growth, April 2003

921 Ramon Castillo and Stergios Skaperdas, All in the Family or Public? Law andAppropriative Costs as Determinants of Ownership Structure, April 2003

922 Peter Fredriksson and Bertil Holmlund, Improving Incentives in UnemploymentInsurance: A Review of Recent Research, April 2003

923 Bernard M.S. van Praag and Adam S. Booij, Risk Aversion and the Subjective TimeDiscount Rate: A Joint Approach, April 2003

924 Yin-Wong Cheung, Kon S. Lai, and Michael Bergman, Dissecting the PPP Puzzle: TheUnconventional Roles of Nominal Exchange Rate and Price Adjustment, April 2003

925 Ugo Trivellato and Anna Giraldo, Assessing the ‘Choosiness’ of Job Seekers. AnExploratory Approach and Evidence for Italy, April 2003

926 Rudi Dornbusch and Stanley Fischer, International Financial Crises, April 2003

927 David-Jan Jansen and Jakob de Haan, Statements of ECB Officials and their Effect onthe Level and Volatility of the Euro-Dollar Exchange Rate, April 2003

928 Mario Jametti and Thomas von Ungern-Sternberg, Assessing the Efficiency of anInsurance Provider – A Measurement Error Approach, April 2003

929 Paolo M. Panteghini and Guttorm Schjelderup, Competing for Foreign DirectInvestments: A Real Options Approach, April 2003

930 Ansgar Belke, Rainer Fehn, and Neil Foster, Does Venture Capital Investment SpurEmployment Growth?, April 2003

931 Assar Lindbeck, Sten Nyberg, and Jörgen W. Weibull, Social Norms and Welfare StateDynamics, April 2003

932 Myrna Wooders and Ben Zissimos, Hotelling Tax Competition, April 2003

933 Torben M. Andersen, From Excess to Shortage – Recent Developments in the DanishLabour Market, April 2003

934 Paolo M. Panteghini and Carlo Scarpa, Irreversible Investments and Regulatory Risk,April 2003

Page 37: A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS T E R P … · 2017-05-05 · CESifo Working Paper No. 950 A MICROFOUNDATION OF PREDATOR-PREY DYNAMICS Abstract Predator-prey relationships

935 Henrik Jacobsen Kleven and Claus Thustrup Kreiner, The Marginal Cost of PublicFunds in OECD Countries. Hours of Work Versus Labor Force Participation, April2003

936 Klaus Adam, George W. Evans, and Seppo Honkapohja, Are Stationary HyperinflationPaths Learnable?, April 2003

937 Ulrich Hange, Education Policy and Mobility: Some Basic Results, May 2003

938 Sören Blomquist and Vidar Christiansen, Is there a Case for Public Provision of PrivateGoods if Preferences are Heterogeneous? An Example with Day Care, May 2003

939 Hendrik Jürges, Kerstin Schneider, and Felix Büchel, The Effect of Central ExitExaminations on Student Achievement: Quasi-experimental Evidence from TIMSSGermany, May 2003

940 Samuel Bentolila and Juan F. Jimeno, Spanish Unemployment: The End of the WildRide?, May 2003

941 Thorsten Bayindir-Upmann and Anke Gerber, The Kalai-Smorodinsky Solution inLabor-Market Negotiations, May 2003

942 Ronnie Schöb, Workfare and Trade Unions: Labor Market Repercussions of WelfareReform, May 2003

943 Marko Köthenbürger, Tax Competition in a Fiscal Union with DecentralizedLeadership, May 2003

944 Albert Banal-Estañol, Inés Macho-Stadler, and Jo Seldeslachts, Mergers, InvestmentDecisions and Internal Organisation, May 2003

945 Kaniska Dam and David Pérez-Castrillo, The Principal-Agent Matching Market, May2003

946 Ronnie Schöb, The Double Dividend Hypothesis of Environmental Taxes: A Survey,May 2003

947 Erkki Koskela and Mikko Puhakka, Stabilizing Competitive Cycles with DistortionaryTaxation, May 2003

948 Steffen Huck and Kai A. Konrad, Strategic Trade Policy and Merger Profitability, May2003

949 Frederick van der Ploeg, Beyond the Dogma of the Fixed Book Price Agreement, May2003

950 Thomas Eichner and Rüdiger Pethig, A Microfoundation of Predator-Prey Dynamics,May 2003