Marciano Siniscalchi Game Theory (Economics 514) Fall 1999 Logistics We (provisionally) meet on Tuesdays and Thursdays, 10:40a-12:10p, in Bendheim 317. I will create a mailing list for the course. Therefore, please send me email at your earliest convenience so I can add you to the list. You do not want to miss important announcements, do you? The course has a Web page at http://www.princeton.edu/~marciano/eco514.html. You should bookmark it and check it every once in a while, as I will be adding material related to the course (including solutions to problems, papers, relevant links, etc.) If you need to talk to me, you can email me at marciano@princeton.edu for an appointment, or just drop by during my regular OH (Wed 1:00-2:30). My office is 309 Fisher. Textbook The main reference for this course is: OSBORNE, M. and RUBINSTEIN, A. (1994): A Course in Game Theory, Cambridge, MA: MIT Press (denoted “OR” henceforth) If you are planning to buy a single book for this course, get this one. However, I will sometimes refer to the following texts (which, incidentally, should be on every serious micro theorist’s bookshelf): MYERSON, R. (1991): Game Theory. Analysis of Conflict, Cambridge, MA: Harvard University Press (denoted “MY” henceforth) FUDENBERG, D. and TIROLE, J. (1991): Game Theory, Cambridge, MA: MIT Press (denoted “FT” henceforth) Plan of the Course Please note: R indicates required readings; O indicates optional readings; and L means that relevant lecture notes will be distributed in class. Lecture notes shall be considered required readings. 1. Introduction 1.1 The main issues Structure of the Course Games as Multiperson Decision Problems R OR Chapter 1 O MY Sections 1.1-1.5 1.2 Zerosum games Minmax theory The Minmax theorem and LP R OR Section 2.5 L Normal—Form Analysis 2.1 Beliefs and Best Responses Dual characterizations of Best Responses Iterating the “best response operator:” rationalizability, iterated weak dominance. R OR Section 2.1 and Chapter 4 O MY Sections 1.8 and 3.1; BERNHEIM, D. (1984): “Rationalizable Strategic Behavior,” Econometrica, 52, 1007-1028. 2.2 Fixed points of the best response operator: Nash equilibrium. Existence and mixed strategies. Interpretation. R OR Sections 2.2-2.4 and 3.1-3.2 3. Games with Incomplete Information 3.1 The basic model The Harsanyi approach Bayesian Nash Equilibrium. Interpretation. R OR Section 2.6 3.2 A closer look: higher-order beliefs Common Priors L 4. Interactive Beliefs and the Foundations of Solution Concepts 4.1 The basic idea: Harsanyi’s model revisited Correlated Equilibrium R OR Section 3.3 L 4.2 Rationality and the Belief operator Common Certainty of Rationality. Equilibrium in Beliefs. L O DEKEL, E. and GUL, F. (1990): “Rationality and Knowledge in Game Theory,” in Advances in Economics and Econometrics, D. Kreps and K. Wallis, eds., Cambridge University Press, Cambridge, UK; TAN, T.C.C. and WERLANG, S.R.C. (1988): “The Bayesian Foundations of Solution Concepts of Games,” Journal of Economic Theory, 45, 370-391. AUMANN, R. and BRANDENBURGER, A. (1995): “Epistemic Conditions for Nash Equilibrium,” Econometrica, 63, 1161-1180. Putting it All Together: Some Auction Theory First- and Second-price auctions Dominance and Equilibrium analysis with private values The Revenue Equivalence Theorem L O MY Section 3.11 5.2 Rationalizability with Incomplete Information Non-equilibrium analysis of auctions Computation! L 6. Extensive Games: Basics 6.1 Extensive games with perfect information Notation(s) and terminology Nash equilibrium R OR Sections 6.1, 6.3, 6.4 Backward Induction and Subgame-Perfect equilibrium The One-Deviation Property Extensive games with perfect but incomplete information Perfect Bayesian equilibrium R OR Section 6.2, 12.3 up to p. 233 Repeated Games: basics General setup and payoff aggregation criteria Automata Nash Folk theorems for infinitely repeated games. R OR Sections 8.1-8.5 7.2 Perfect folk theorems for infinitely repeated games Perfect folk theorems for finitely repeated games R OR Sections 8.8-8.10 8. Extensive Games: details 8.1 General Extensive games: imperfect information. Relationship between normal and extensive form. Mixed and Behavioral strategies. Kuhn’s Theorem. Perfect and Imperfect Recall R OR Chapter 11 Sequential rationality and off-equilibrium beliefs Trembling-Hand Perfect equilibrium Consistent Assessments and Sequential Equilibrium R OR Sections 12.1-12.2, 12.5 O KREPS, D. and WILSON, R. (1982): “Sequential equilibria,” Econometrica, 50, 863-894; SELTEN, R. (1975): “A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory, 4:25-55. 9. Applications of Sequential Equilibrium 9.1 The Chain Store Paradox Modelling Reputation Comments: (1) Backward Induction; (2) Plausible beliefs R KREPS, D. and WILSON, R. (1982): “ Reputation and Imperfect Information,” Journal of Economic Theory 27, 253-279 O ROSENTHAL, R. (1981): “Games of Perfect Information, Predatory Pricing and the Chain-Store Paradox,” Journal of Economic Theory 25:92-100. 9.2 Sequential and Perfect Bayesian Equilibrium S.E. and P.B.E. in applications An Example: Insider Trading R OR, Section 12.3 KYLE, A. (1985) : “Continuous Auctions and Insider Trading,” Econometrica 53, 1315-1334. 10. Sequential Equilibrium: A Critical Look 10.1 Consistency The Centipede Game and Backward Induction Strategy and Plans of Action. Variants of sequential rationality. Weak Sequential Equilibrium R RENY, P. (1992): “Backward Induction, Normal Form Perfection, and Explicable Equilibria,” Econometrica 60:627-649. 10.2 Interactive Beliefs Models for Dynamic Games Backward Induction and Common Certainty of Rationality Weak Rationalizability L O BEN-PORATH, E. (1997): “Rationality, Nash Equilibrium, and Backwards Induction In Perfect-Information Games,” Review of Economic Studies 64, 23-46 11. Extensive Games: Refinements 11.1 Forward induction: outside options, burning money. Forward and Backward induction. Iterated weak/conditional dominance and Extensive-Form rationalizability. R BEN-PORATH, E. and DEKEL, E. (1992): “Signalling Future Actions and the Potential for Sacrifice,” Journal of Economic Theory 57:36-51. L O PEARCE, D. (1984): “Rationalizable Strategic Behavior and the Problem of Perfection,” Econometrica 52:1029-1050. BATTIGALLI, P. (1997): “On Rationalizability in Extensive Games,” Journal of Economic Theory 74:40-61. 11.2 Signalling Games and specialized versions of Forward Induction The Intuitive Criterion: a simple test of “reasonableness.” “Monotonicity” of signals: Dn, divinity and friends. R CHO, I. and KREPS, D. (1987): “Signalling Games and Stable Equilibria,” Quarterly Journal of Economics 102: 179-221. 12. Invariance and Normal-Form refinements 12.1 The Interplay between Normal and Extensive-form analysis Invariance Perfect and Proper Equilibria. Proper and Sequential equilibria. L 12.2 Strategic Stability and the “axiomatic approach” A list of desiderata, and the need for set-valued solutions. “True perfection” and the “Nearby games, Nearby equilibria Principle.” R KOHLBERG, E. and MERTENS, J-F., (1986): “On the Strategic Stability of Equilibria,” Econometrica 54, 1003-1037.