Economics 286 Jonathan LevinSpring 2006 Stanford University

Game Theory Syllabus

Overview. This is an advanced course in game theory, intended for students whoare interested in pursuing micro theory research or who want a good theory back-ground to do applied work. The course will cover a combination of standard resultsand current research topics. The prerequisite is familiarity with the basic ideas ofgame theory – Nash equilibrium, subgame perfection, incomplete information –as introduced in Economics 203. Please talk to me if you haven’t taken Economics203 or 160 or another equivalent.

Logistics. The class meets MW 9:00—10:50 in Econ 218. I plan to have officehours M 3:15—5 in my Economics Department office (Landau 240). You can alsocontact me to make an appointment for some other time. My email address isjdlevin@stanford.edu. I’ll post assignments, lecture notes, etc. on the StanfordCoursework class web page.

Assignments and Grading. There will be four problem sets and a final exam.Grades are based on a weighted average of assignments (40%) and the exam (60%).The assignments will be spaced evenly over the quarter. I encourage you to collabo-rate so long as solutions are written up individually. I’ll post solutions on the courseweb page. The grader for the class is Xiaochen Fan (xfan@stanford.edu) – pleasedon’t harass her unnecessarily. The exam will have a 24 hour take-home format,with a several day window for taking it.

Reading. I will hand out notes for all the lectures. The lectures notes will havedetailed references; virtually all the papers can be downloaded easily. There are alsoseveral books you may find useful.

Fudenberg, D. and J. Tirole, Game Theory, MIT Press, 1992.

Osborne, M. and A. Rubinstein, A Course in Game Theory, MIT Press, 1994.

Mailath, G. and L. Samuelson, Repeated Games and Reputations: Long-Run Rela-tionships, Oxford, 2006.

The first two are general texts and have substantial overlap. Both are excellent, butclose to fifteen years old. The Mailath-Samuelson book is not-yet released; you canfind selected chapters on George Mailath’s webpage at Penn.

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Outline of Topics

1. Solution Concepts (2 lectures)

FT, chapter 2; OR, chapters 2—4.

Bernheim, D. (1984) “Rationalizable Strategic Behavior,” Econometrica, 52,1007-1028.

Pearce. D. (1984) “Rationalizable Strategic Behavior and the Problem ofPerfection,” Econometrica, 52, 1029-1050.

Aumann, R. (1987) “Correlated Equilibrium as an Extension of BayesianRationality,” Econometrica, 55, 1-18.

Brandenburger, A. and E. Dekel (1987): “Rationalizability and CorrelatedEquilibria,” Econometrica, 55, 1391—1402.

Gul, F. (1998) “A Comment on Aumann’s Bayesian View,” Econometrica,66.

Fudenberg, D. and D. Levine (1993) “Self-Confirming Equilibrium,” Econo-metrica, 61, 523- 546.

Dekel, E., D. Fudenberg and D. Levine (2004) “Learning to Play BayesianGames,” Games and Econ. Behav., 46, 282-303.

2. Common Knowledge and Common Priors (2 lectures)

OR, chapter 5.

Samuelson, L. (2004) “Modeling Knowledge in Economic Analysis,” J. Econ.Lit., 62, 367-403.

Aumann, R. and A. Brandenburger (1995) “Epistemic Conditions for NashEquilibrium,” Econometrica, 63, 1161-1180.

Aumann, R. (1976) “Agreeing to Disagree,” Ann. of Stat.

Milgrom, P. and N. Stokey (1982) “Information, Trade and Common Knowl-edge,” J. Econ. Theory, 26, 177-227.

Harrison, M. and D. Kreps (1978): “Speculative Investor Behavior in a StockMarket with Heterogeneous Expectations,” Quart. J. Econ, 92, 323-336.

3. Supermodular Games and Global Games (2 lectures)

Milgrom, P. and J. Roberts (1990) “Rationalizability and Learning in Gameswith Strategic Complementarities,” Econometrica, 58, 1255-1277.

Carlsson, H. and E. van Damme (1993) “Global Games and EquilibriumSelection,” Econometrica, 61, 989-1018.

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Morris, S. and H. Shin (1998) “Unique Equilibrium in a Model of Self-Fulfilling Attacks,” Amer. Econ. Rev., 89, 587—597.

Morris, S. and H. Shin (2002) “The Social Value of Public Information,”Amer. Econ. Rev., 92, 1521-1534.

Morris, S. and H. Shin (2003) “Global Games: Theory and Applications,” inAdvances in Economics and Econometrics, Cambridge University Press.

Abreu, D. and M. Brunnermeier (2003) “Bubbles and Crashes,” Economet-rica, 71, 173—204.

4. Repeated Games (4 lectures)

Fudenberg and Tirole, chapter 5.

Osborne and Rubinstein, chapter 8.

Abreu, D. “On the Theory of Infinitely Repeated Games with Discounting,”Econometrica.

Abreu, D. D. Pearce and E. Stacchetti (1990) “Toward a Theory of Dis-counted Repeated Games with Imperfect Monitoring,” Econometrica, 60,1041-1063.

Fudenberg, D. and E. Maskin (1986) “The Folk Theorem for Repeated Gameswith Discounting or with Incomplete Information,” Econometrica.

Fudenberg, D. D. Levine and E. Maskin (1994) “The Folk Theorem withImperfect Public Information,” Econometrica, 64, 997-1039.

Levin, J. (2003) “Relational Incentive Contracts,” Amer. Econ. Rev.

Sekiguchi, T. (1997) “Efficiency in Repeated Prisoners’ Dilemma with PrivateMonitoring,” J. Econ. Theory, 76, 345—361.

Ely, J. and J. Valimaki (2002) “A Robust Folk Theorem for the Prisoners’Dilemma,” J. Econ. Theory.

Mailath, G. and S. Morris (2002) “Repeated Games with Almost-Public Mon-itoring,” J. Econ. Theory.

Matsushima, H. (2004) “Repeated Games with Private Monitoring: TwoPlayers,” Econometrica.

Ely, J., J. Horner, and W. Olszewski (2005) “Belief-free Equilibria in Re-peated Games,” Econometrica.

Horner, J. and W. Olszewski (2006) “The Folk Theorem for Games withPrivate Almost-Perfect Monitoring,” Econometrica.

5. Reputation (2-3 lectures)

Kreps, D. and R. Wilson (1982) “Reputation and Imperfect Information,” J.Econ. Theory, 27, 253-179.

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Milgrom, P. and J. Roberts (1982) “Predation, Reputation, and Entry De-terrence,” J. Econ. Theory, 27, 280-312.

Fudenberg, D. and D. Levine (1989) “Reputation and Equilibrium Selectionin Ganes with a Patient Player,” Econometrica, 57, 759-778.

Schmidt, K. (1993) “Reputation and Equilibrium Characterization in Re-peated Games with Conflicting Interests,” Econometrica, 61, 325-351.

Tiroloe, J. (1996) “A Theory of Collective Reputations,” Rev. Econ. Studies.

Ely, J. and J. Valimaki (2002) “Bad Reputation,” Quarterly J. Econ.

Tadelis, S. (2003) “The Market for Reputations as an Incentive Mechanism,”J. Pol. Econ.

Mailath, G. and L. Samuelson (2001) “Who Wants a Good Reputation,” Rev.Econ. Studies.

Abreu, D. and F. Gul (2001) “Bargaining and Reputation,” Econometrica.

Cripps, M., G. Mailath and L. Samuelson (2004) “Imperfect Monitoring andImpermanent Reputations,” Econometrica.

Abreu, D. and D. Pearce (2005) “Reputational Wars of Attrition with Com-plex Bargaining Postures,” Working Paper.

6. Learning in Games (2 lectures)

Fudenberg, D. and D. Levine, Theory of Learning in Games, MIT Press,1998.

Kalai, E. and E. Lehrer (1993) “Rational Learning Leads to Nash Equilib-rium, Econometrica, 61, 1019—1045.

Nachbar, J. (1997) “Prediction, Optimization, and Learning in RepeatedGames,” Econometrica, 65, 275-309.

Erev, I. and A. Roth (1998) “Predicting how People Play Games: Rein-forcement Learning in Experimental Games with Unique Mixed StrategyEquilibria,” Amer. Econ. Rev., 85, 848—881.

Hart, S. and A. Mas-Colell (2003) “Uncoupled Dynamics Do Not Lead toNash Equilibrium,” Amer. Econ. Rev., 93, 1830-1836.

Bereby-Meyer, Y. and A. Roth (2006) “Learning in Noisy Games: PartialReinforcement and the Sustainability of Cooperation,”Amer. Econ. Rev.

7. Behavioral Game Theory: Experiments (1 lecture)

Camerer, C. (2003) Behavioral Game Theory: Experiments on Strategic In-teraction, Princeton: Princeton University Press, 2003.

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Crawford, V. (1997) “Theory and Interaction in the Analysis of StrategicInteraction,” Advances in Economics and Econometrics, Seventh WorldCongress of the Econometric Society, Volume 1.

Nagel, R. (1995) “Unraveling in Guessing Games: An Experimental Study,”Amer. Econ. Rev., 85, 1313—1326.

Costa-Gomes, M., V. Crawford and B. Boseta (2001) “Cognition and Behav-ior in Normal-Form Games: An Experimental Study,” Econometrica.

Costa-Gomes, M. and V. Crawford, “Cognition and Behavior in Two-PersonGuessing Games: An Experimental Study,” Working Paper.

8. Behavioral Game Theory: Models (2-3 lectures)

Geanakoplos, J., D. Pearce and E. Stacchetti (1989) “Psychological Gamesand Sequential Rationality,” Games Econ. Behav., 1, 60-79.

Rabin, M. (1993) “Incorporating Fairness into Game Theory and Economics,”Amer. Econ. Rev., 85, 1281-1302.

Fehr, E. and K. Schmidt (1999) “A Theory of Fairness, Competition andCooperation,” Quart. J. Econ. 114, 817-868.

Bernheim, D. and A. Rangel (2004) “Addiction and Cue-Triggered DecisionProcesses,” Amer. Econ. Rev.

Fudenberg, D. and D. Levine (2005) “A Dual Self Model of Impulse Control,”Working Paper.

Koszegi, B. and M. Rabin (2006) “A Model of Reference Dependent Prefer-ences,” Quart. J. Econ.

Heidhues, P. and B. Koszegi (2006) “The Impact of Consumer Loss Aversionon Pricing,” Working Paper.

Dewatripont, M. and J. Tirole (2005) “Modes of Communication,” J. Pol.Econ.

Eyster, E. and M. Rabin (2005) “Cursed Equilibrium,” Econometrica.

Esponda, I. (2006) “Behavioral Equilibrium in Economies with Adverse Se-lection,” Working Paper.

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