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University of Wisconsin-Madison Department of Economics ECON 809 Spring 2003 Course Plan Prof. R. Deneckere

Game Theory

General References

* Fudenberg, D. and J. Tirole, Game Theory, MIT Press, Cambridge, 1991. * Fudenberg, D. and D. Levine, "The Theory of Learning in Games," MIT Press, Cambridge, 1998.

Myerson, R. (1991), Game Theory, Harvard University Press, London. Osborne, M. and A. Rubinstein (1994), A Course in Game Theory, MIT Press, Cambridge, Massachusetts. Van Damme, E. (1991), Stability and Perfection of Nash Equilibria, Springer Verlag, Berlin. Moulin, H. (1981), Game Theory for the Social Sciences, New York University Press, New York. Kreps, D. (1990), A Course in Microeconomic Theory, Princeton University Press, Princeton, New Jersey. Owen, G. (1982), Game Theory, Academic Press, New York.

I. Introduction

* Aumann, R. (1985), "What is Game Theory Trying to Accomplish?," in Frontiers of Economics (K. Arrow and S. Honkapohja, Eds.), Basil Blackwell, Oxford, pp. 28-76. Aumann, R. (1987), "Game Theory," in The New Palgrave, Vol. 2 (J. Eatwell, M. Milgate and P. Newman, Eds.), Macmillan, London, pp. 460-482. Kreps, D. (1990), Game Theory and Economic Modelling, Carendon Press, Oxford.

II. Decision Theory

Expected utility Theorem; Violations of Expected Utility maximization; Domination Theorems; Alternatives to expected Utility Maximization * Myerson (1991), Ch. 1. * Kreps, (1990), Chs. 3 and 4. Kreps, D. (1988), Notes on the Theory of Choice, Westview Press, Boulder, Colorado. Machina, M. (1987), "Choice Under Uncertainty : Problems Solved and Unsolved," Journal of Economic Perspectives, 1(1), pp. 121-154. Epstein, L. (1997), "Preference, Rationalizability and Equilibrium," Journal of Economic-Theory, 73(1), pp. 129.

Dekel, E., Safra, Z. and U. Segal (1991), "Existence and Dynamic Consistency of Nash Equilibrium with Nonexpected Utility Preferences," Journal of Economic Theory, 55(2), pp. 229-46. Lo, K.-C. (1999), "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior," 28(2), pp. 256-270.

III. Strategic Form Games : Complete Information

Dominant Strategy Equilibrium Iterated Strict Dominance and Rationalizability

* Fudenberg and Tirole, Sections 1.1 and 2.1 * Osborne and Rubinstein, Sections 4.1 and 4.2.

Iterated Weak Dominance * Osborne and Rubinstein, Section 4.3. * Marx, L. and J. Swinkels (1997), "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, 18(2), pp. 219-45. * Marx, L. and J. Swinkels (2000), "Order Independence for Iterated Weak Dominance,"Games and Economic Behavior; 31(2), pp. 324-29. Börgers, T. (1994), "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, 64(1), pp.265-276. Nash Equilibrium Definition and Interpretation Existence of pure strategy equilibria in infinite games Existence of mixed strategy equilibria in finite games Existence of mixed strategy equilibria in infinite games * Fudenberg and Tirole, Section 1.2 * Osborne and Rubinstein, Sections 2.1-2.5 and 3.1-3.2. Myerson, Ch. 3. Existence of mixed strategy equilibria in discontinuous games * Fudenberg and Tirole, Section 12.2. * Reny, P. (1999), "On the Existence of Pure and Mixed Strategy Nash Equilibrium in Discontinuous Games," Econometrica,; 67(5), pp. 1029-1056. Supermodular Games * Fudenberg and Tirole, Section 12.3. Milgrom, P. and J. Roberts (1990), "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, 58(6), pp. 1255-77. Milgrom, P. and C. Shannon (1994), "Monotone Comparative Statics," Econometrica, 62(1), pp. 157-80. Properties of Nash equilibrium * Fudenberg and Tirole, Sections 1.3 and 12.1 Strategic Form Refinements Trembling hand perfection

Properness * Fudenberg and Tirole, Sections 8.6 * Myerson, Sections 5.1-5.5. Essential Equilibria, strictly perfect equilibria Kohlberg-Mertens stability and forward induction * Fudenberg and Tirole, Ch. 11 * Myerson, Section 5.6-5.8. * Kohlberg, E. and J.-F. Mertens (1986), "On the Strategic Stability of Equilibria," Econometrica, 54(5), pp. 1003-1037. Ben-Porath, E. and E. Dekel (1992), "Signaling Future Actions and the Potential for Sacrifice," Journal of Economic Theory, 57(1), pp. 36-51. Dekel, E. (1990), "Simultaneous Offers and the Inefficiency of Bargaining: A Two-Period Example," Journal of Economic Theory, 50(2), pp. 300-308. Evolutionary Stable Strategies * Fudenberg and Levine (1998), Chs. 1 and 3. Correlated Equilibrium * Fudenberg and Tirole , Sections 2.1 and 2.2 * Osborne and Rubinstein, Section 3.3 * Brandenberger, A. and E. Dekel (1987), "Rationalizability and Correlated Equilibria," Econometrica, 55, pp. 1391-1402. Myerson, Ch. 6

IV. Bayesian Games and Mechanism Design

Bayesian Games : Dominance, Bayesian Equilibrium, Infinite Bayesian Games * Fudenberg and Tirole, Ch. 6. * Milgrom, P. and R. Weber, "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, 10, pp. 619-631. * Mertens, J.-F. and S. Zamir (1985), "Formulation of Bayesian Analysis for Games with Incomplete Information," International Journal of Game Theory, 10, pp. 619-632. Brandenburger, A. and E. Dekel (1993), "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, 59(1), 189-198. Mechanism Design : Revelation Principle, Characterization of Incentive Feasible Set, Optimal Mechanisms, Inefficiency Theorems, Dominant Strategy Mechanisms * Fudenberg and Tirole, Ch. 7 * Myerson, Sections 6.3-6.5

V. Dynamic Games of Complete Information

Extensive Form Games, Strategic Form representation, Mixed and Behavioral Strategies, Kuhn's Theorem, Existence of Equilibrium in Behavioral Strategies

* Fudenberg and Tirole, Sections 3.3 and 3.4 * Myerson, Sections 4.1 and 4.2 Piccione, M. and A. Rubinstein (1997), "On the Interpretation of Decision Problems with Imperfect Recall" Games and Economic Behavior, 20(1), pp. 3-24. Piccione, M. and A. Rubinstein (1997), "The Absent-Minded Driver's Paradox: Synthesis and Responses," Games and Economic Behavior, 20(1), pp. 121-30. Backward induction and Subgame Perfection, Games of Perfect Information and Zermelo's Theorem, Multi-stage Games with Observed Actions, Principle of Optimality * Fudenberg and Tirole, Sections 3.5-3.6 * Osborne and Rubinstein, Ch. 6 Alternating-offer bargaining, iterated conditional dominance * Fudenberg and Tirole, Sections 4.4 and 4.6. * Osborne and Rubinstein, Ch. 7. Repeated Games, Folk Theorems, Renegotiation * Fudenberg and Tirole, Ch. 5. * Osborne and Rubinstein, Ch. 8 * Abreu, D. P.-K. Dutta, and L. Smith (1994), "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, 62(4), pp. 939-48. Relationship between the extensive form and the normal form of a game * Mailath, G., L. Samuelson and J. Swinkels (1994), "Normal Form Structures in Extensive Form Games," Journal of Economic Theory, 64(2), pp. 325-71. * Mailath, G., L. Samuelson and J. Swinkels (1993),"Extensive Form Reasoning in Normal Form Games," Econometrica, 61(2), pp. 273-302. Thomson, F. (1952), "Equivalence of Games in Extensive Form," Rand Memo RM-759, reprinted in Classics in Game Theory, H. W. Kuhn (Ed.), Priceton University Press, New Jersey, 1952, pp. 36-45. Extensive Form Correlated Equilibria Myerson, Sections 6.8 and 6.9 Myerson, R. (1986), "Multistage Games with Communication," Econometrica, 54(2), pp. 323-358.

VI. Dynamic Games of Incomplete Information

Extensive form perfection, Sequential Equilibrium * Fudenberg and Tirole, Sections 8.1-8.3 Myerson, Ch. 4 Strategic Stability and Forward Induction

Fudenberg and Tirole, Ch. 11 Van Damme (1991), Ch. 10

VII. Bounded Rationality

Rubinstein, A. (1998), "Modelling Bounded Rationality," MIT Press. Abreu, D. and A. Rubinstein (1988), "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, 56(6), pp. 1247-1258. Banks, J. and D. Sundaram (1990), "Repeated Games, Finite Automata, and Complexity," Games and Economic Behavior, 2(2), pp. 97-117. Piccione, M. and A. Rubinstein (1997), "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, 20(1), pp. 3-24. Aumann, R. and S. Sorin, "Cooperation and Bounded Recall," Games and Economic Behavior, 1(1), pp. 539.

VIII. Evolutionary Game Theory

Fictitious Play, stochastic fictitious play, mutations, self-confirming equilibrium Fudenberg and Levine (1998), Chs. 2, 4-6 Kandori, M., G. Mailath and R. Rob (1993), "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, 61(1), 29-56. Samuelson, L. and J. Zhang (1992), "Evolutionary Stability in Asymmetric Games," Journal of Economic Theory, 57(2), pp. 363-391. Samuelson, L. and G. Noldeke (1993), "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, 425-454.

IX. Common Knowledge and games

Knowledge, Common Knowledge, Agreeing to Disagree, No-Speculation Theorems, Almost Common Knowledge Fudenberg and Tirole, Ch. 14 Osborne and Rubinstein, Ch. 5. Rubinstein, A. (1989), "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge"," American Economic Review,79(3), pp. 385-91. Brandenburger, A. (1992), "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, 6(4), pp. 83-101.

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