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7/21/2019 Game Theory Presentation 1229367921111224 2
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Abbas Keramati ( Assistant Professor)
University of Tehran MBAFall 2008
Game Theory Quantitative Analysis for Decision Making
M.hotbi
M.Pa!ho"h #iya
7/21/2019 Game Theory Presentation 1229367921111224 2
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Title
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Outline
What is Game Theory? History of Game Theory
Applications of Game Theory
Key Elements of a game Types of games
Nash Equilibrium (NE
!ure "trategies # $i%e& "trategie
'players ero)"um games
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hat is Game Theory?
*n strategic games+ agents choose
strategies that ,ill ma%imi-e theirreturn+ gi.en the strategies theother agents choose/
The mathematics of humaninteractions
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History of Game Theory
.on Neumannwrote a key paper in1928
1944 !Theory of Games and Economic
Behavior"y von #eumann and$orgenstern
19%& Nashinvents concept o' #as(e)uili"rium
*ame t(eory "ooms a'ter t(is+
1994 Harsanyi,Nash, and "eltenwin #o"el ri-e in economics 'or game
t(eory work
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$at(ematics
omputer /cience
0iology
conomics
olitical /cience
nternational
3elations
(ilosop(y
syc(ology
Law
$ilitary /trategy
$anagement
/ports
*ame laying
Applications of GameTheory
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Key Elements of a game
!layers (o is interacting5
"trategies (at are t(eir optio
!ayo0s (at are t(eir incentive
*nformation (at do t(ey know 1ationality 6ow do t(ey t(ink5
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Types of games
2ooperati.e or non)cooperati.e
ero sum an& non)-ero sum
"imultaneous an& sequential
!erfect information an& imperfect
information
3inite # *n4nite "trategies
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0
:1 :2 $inimum
;1 1& < =12
$a%imum 1& >5
6
An E%ample7
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Nash Equilibrium (NE
A players best strategy isA players best strategy is
that strategy that maximizesthat strategy that maximizes
that players payoff (utility),that players payoff (utility),
knowing the strategy's of theknowing the strategy's of the
other players.other players.
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')players ero)"umgames
-1 , 1 1 , -1
1 , -1 -1 , 1Player
Player !
enny $atc(ing ac( o' t(e two players (as a penny.
Two players must simultaneously c(oose w(et(er
to s(ow t(e 6ead or t(e Tail.
0ot( players know t(e 'ollowing rules =' two pennies matc( ?"ot( (eads or "ot(
tails@ t(en player 2 wins player 1As penny.
=Bt(erwise, player 1 wins player 2As penny.
"ail
#ea$
"ail
#ea$
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!risoner8s 9ilemma
#o communication
= /trategies must "e undertaken wit(out
t(e 'ull knowledge o' w(at t(e ot(erplayers ?prisoners@ will do.
layers ?prisoners@ develop dominant strategies
"ut are not necessarily t(e "est one.
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Ted
on'ess #ot on'ess
on'ess
0ill
#ot on'ess
0ot( get %years
1 year 'or0ill
1& years 'orTed
1& years 'or0ill
1 year 'orTed
0ot( get C
years
ayoD $atri 'orrisonerAs Eilemma
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An E%ample of
$i%e& "trategy game
0
0"elieves
0
doesnAt"elieve
"luDs 1 &
doesnAt"luD
& &.%
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Lorem ipsum dolor sit amet,consectetuer adipiscing elit. Vivamus etmagna. Fusce sed sem sed magna
suscipit egestas.
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No, let8s !lay This Game
Pirate Game
A
B
D
C
E
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Nash8s Equilibrium
T(is e)uili"rium occurs w(en eac( playerAsstrategy is optimal, knowing t(e strategys o' t(eot(er players.
playerAs "est strategy is t(at strategy t(atmaimi-es t(at playerAs payoD ?utility@, knowingt(e strategys o' t(e ot(er players.
/o w(en eac( player wit(in a game 'ollows t(eir
"est strategy, a #as( e)uili"rium will occur.
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9e4nition7 NashEquilibrium
Given others
choices, layer icannot !e !etter"off
if she #eviates from
si$
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Nashs Equilibrium cont.:
Bayesian Nash Equilibrium
T(e #as( )uili"rium o' t(e imper'ect=in'ormation game
% 0ayesian )uili"rium is a set o' strategies suc(t(at eac( player is playing a "est response, givena particular set o' "elie's a"out t(e move "ynature.
% ll players (ave t(e same prior "elie's a"out t(epro"a"ility distri"ution on natureAs moves.
% /o 'or eample, all players t(ink t(e odds o' player 1"eing o' a particular type isp, and t(e pro"a"ility o' (er"eing t(e ot(er type is 1-p
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Eiit and #ale"uD ThinkingStrategically
Eutta
Strategies and Games: Theoryand Practice
www.gamet(eory.net
$efrences
http://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=bookshttp://www.amazon.com/exec/obidos/tg/detail/-/0262041693/qid=1076968166/sr=1-1/ref=sr_1_1/103-9367263-5214241?v=glance&s=books