Amanda Friedenberg
ECN 791: Topics in Game Theory
Fall 2016
Course Syllabus
This is a second-year course on game theory. The course will cover both classical results and modern
research. The course is intended to serve both students interested in developing game theory, as
well as students interested in applying game theory to other areas.
Grading Grading of the course will be determined by take-home problem sets, an in-person
problem set, and a referee report. Dates of these deliverables will be determined as the term
progresses.
Take-Home Problem Sets: There will be 2-3 take-home problem sets. Taken together, they comprise
60% of the final grade. You will have two weeks to complete each problem set, from the time it
is handed out. You should plan on devoting the full two weeks to each problem set: The problem
sets will not be problem sets that can be completed overnight.
In-Person Problem Sets: There will be one in-person problem set which will comprise 20% of the
final grade. You will be assigned a proof to prepare in advance of class and you will be expected
to explain the proof to your classmates. We will not continue class until we have successfully
completed a proof (as opposed to a ‘sketch of an argument’). As a consequence, this may require
scheduling extra class time.
Referee Report: I will assign a working paper and ask you to prepare a referee report on it. The
referee report should be ‘standard form,’ where you evaluate the paper for a top theory journal.
The report need not be long, but should be thoughtful. This will comprise 20% of the grade.
(William Thomaon’s “A Guide for the Young Economist” is an excellent source, to learn how to
write referee reports.)
Background Readings There is no formal textbook for the course. However, at times, it will
be useful to have a textbook on your shelf. Here, are some recommended textbooks:
• Osborne, M., and A. Rubinstein, A Course in Game Theory, 1994.
• Fudenberg, D, and J. Tirole, Game Theory, 1991.
The first of these is available electronically. There are also several relevant specialized textbooks:
• Battigalli, P., Brandenburger, A., Friedenberg, A., and M. Siniscalchi, Epistemic Game Theory: Reasoning About Strategic Uncertainty, partial manuscript.
• Mailath, G., and L. Samuelson, Repeated Games and Reputations, 2006.
• Mertens, J.F., Sorin, S., and S. Zamir, Repeated Games, 2015.
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It may also be a good idea to get a hold on a couple of math books. Here are two recommendations.
• Aliprantis, C., and K. Border, Infinite Dimensional Analysis, 2006.
• Billingsley, P., Probability and Measure, 1995.
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Reading List: Fall 2016
Below is a reading list for the the course. The plan is to focus on papers labelled [*]. Other reading
should be viewed as either background reading or more advanced reading.
1. Foundational Material
Structure of Games
* Kuhn, H.W., “Extensive games and the problem of information,” Classics in Game Theory,
46–68, 1953, Princeton University Press.
• Brandenburger, A., A Note on Kuhn’s Theorem, in Interactive Logic, Proceedings of the 7th
Augustus de Morgan Workshop, London, edited by Johan van Benthem, Dov Gabbay, and
Benedikt Loewe, Texts in Logic and Games 1, ISBN: 9789053563564, Amsterdam University
Press, 2007, 71-88
• Thompson, “Equivalence of games in extensive form,” Classics in Game Theory, 36–45, 1952,
Princeton University Press.
• Elmes, S., and P. Reny, “On the strategic equivalence of extensive form games,” Journal of
Economic Theory, 62, 1, 1–23, 1994.
* Harsanyi, “Games with Incomplete Information Played by “Bayesian” Players, I-III,” Management Science, 1967-1968.
Type Structures and Hierarchies of Beliefs
* Battigalli, P., Brandenburger, A., Friedenberg, A., and M. Siniscalchi, Epistemic Game Theory: Reasoning About Strategic Uncertainty, Chapters 2-4.
* Siniscalchi, M., Epistemic Game Theory: Beliefs and Types, The New Palgrave Dictionary
of Economics.
• Mertens, J.F., and S. Zamir, “Formulation of Bayesian analysis for games with incomplete
information”, International Journal of Game Theory, 14, 1, 1-29, 1985.
* Brandenburger, A., and E. Dekel, Hierarchies of beliefs and common knowledge, Journal of
Economic Theory, 59, 1993.
• Brandenburger, A., “On the existence of a “complete” possibility structure,” in Cognitive
Processes and Economic Behaviour, 2003.
• Friedenberg, A., “When do type structures contain all hierarchies of beliefs?,” Games and
Economic Behavior, 68, 108-129, 2010.
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Knowledge Structures and the Common Prior Assumption
* Aumann, R.J., “Agreeing to disagree,” The annals of statistics, 4, 6, 1236-1239, 1976.
• Milgrom, P., and N. Stokey, “Information, trade and common knowledge,” Journal of Economic Theory, 26, 1, 17-27, 1982.
• Green, E., “Events Concerning Knowledge,” 2012.
• Gul, F. “A comment on Aumann’s Bayesian View.” Econometrica, 923-927, 1998.
2. Epistemic Game Theory: Strategic Uncertainty
Simultaneous Move Games
* Battigalli, P., Brandenburger, A., Friedenberg, A., and M. Siniscalchi, Epistemic Game Theory: Reasoning About Strategic Uncertainty, Chapters 6-7.
* Dekel, E., and M. Siniscalchi, Epistemic Game Theory, 2013.
* Pearce, D., “Rationalizable strategic behavior and the problem of perfection,” Econometrica,
52, 4, 1029-1050, 1984.
* Bernheim, D., “Rationalizable strategic behavior,” Econometrica, 52, 4, 1007-1028, 1984.
* Brandenburger, A., and E. Dekel, “Rationalizability and Correlated Equilibria,” Econometrica, 1391-1402, 1987.
• Tan, T.C., and S.R. Werlang, “The Bayesian foundations of solution concepts of games,”
Journal of Economic Theory, 45, 2, 370-391, 1988.
• Aumann, R.J., “Correlated equilibrium as an expression of Bayesian rationality,” Econometrica, 55, 1, 1-18, 1897.
• Brandenburger, A., and A. Friedenberg, “Intrinsic Correlation in Games,” Journal of Economic Theory, 141, 2008, 28-67
• Milgrom, P. and J. Roberts, “Rationalizability, learning, and equilibrium in games with strategic complementarities,” Econometrica, 1255-1277, 1990.
Epistemic Justification of Nash Equilibrium
• Battigalli, P., Brandenburger, A., Friedenberg, A., and M. Siniscalchi, Epistemic Game Theory: Reasoning About Strategic Uncertainty, Chapter 8.
• Dekel, E., and M. Siniscalchi, Epistemic Game Theory, 2013.
• Aumann, R.J., and A. Brandenburger, Econometrica, Vol. 63, 1995, 1161-1180
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Extensive Form Games
* Ben Porath, E., “Rationality, Nash equilibrium and backwards induction in perfect-information
games,” The Review of Economic Studies, 64, 1, 23-46, 1997.
* Battigalli, P., and M. Siniscalchi, “Strong belief and forward induction reasoning,” Journal
of Economic Theory, 106, 2, 358-391, 2002.
• Battigalli, P., and M. Siniscalchi, “Hierarchies of conditional beliefs and interactive epistemology in dynamic games,” Journal of Economic Theory, 88, 1, 188-230, 1999.
• Battigalli, P., and A. Friedenberg, “Context-Dependent Forward Induction Reasoning,” Theoretical Economics, 2012.
• Battigalli, P., “On rationalizability in extensive games,” Journal of Economic Theory, 74, 1,
40-61, 1997.
Admissibility
• Samuelson, L., “Dominated strategies and common knowledge,” Games and Economic Behavior, 4, 2, 284-313, 1992.
• Brandenburger, A., A. Friedenberg, H.J. Keisler, “Admissibility in Games,” Econometrica,
Vol. 76, 2008, 307-352
• Keisler, H.J., and B.S. Lee, “Common Assumption of Rationality,” 2010.
• Lee, B.S., “Admissibility and Assumption,” Journal of Economic Theory, 2016.
• Brandenburger, A., and A. Friedenberg, “Self-Admissible Sets,” Forthcoming in Journal of
Economic Theory.
Applications
• Pomatto, L., “Stable Matching under Forward Induction Reasoning,” 2015.
• Friedenberg, A., “Inefficient Delay: The Role of Second-Order Optimism,” 2014.
• Harrington, J., “A Theory of Collusion with Partial Mutual Understanding,” 2015.
• Penta, A. and M. Ollar, “Full Implementation and Belief Restrictions,” 2016.
3. Incomplete Information: Foundations and Robustness
Solution Concepts: Bayesian Equilibrium and Rationalizability
• Dekel, E., D. Fudenberg and S. Morris, “Interim Correlated Rationalizability,” Theoretical
Economics, 2, 15-40, 2007.
• Friedenberg, A., and M. Meier, “The Context of the Game,” Economic Theory, forthcoming.
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Robustness to Misspecifying Hierarchies of Beliefs
• Morris, S., and H.S. Shin, “Global Games: Theory and Applications,” Advances in Economics
and Econometrics: theory and applications, Eighth world Congress, 1, 56-114, 2003.
• Geanakoplos, J. and H. Polemarchakis, “We Can’t Disagree Forever,” Journal of Economic
Theory, 28, 192-200, 1982.
• Rubinstein, A., “The Electronic Mail Game: Strategic Behavior Under” Almost Common
Knowledge,” The American Economic Review, 79, 385-391, 1989.
* Carlsson, H., and E. Van Damme, “Global games and equilibrium selection,” Econometrica,
61, 5, 989-1018, 1993.
* Kajii, A. and S. Morris, “The robustness of equilibria to incomplete information,” Econometrica, 65, 6, 1283-1309, 1997.
* Frankel, D., S. Morris, and A. Pauzner, “Equilibrium selection in global games with strategic
complementarities,” Journal of Economic Theory, 108, 1–44, 2003.
* Weinstein, J., and M. Yildiz, “A structure theorem for rationalizability with application to
robust predictions of refinements,” Econometrica, 75, 2, 2007.
• Y.C. Chen, S. Takahashi, and S. Xiong, “The Robust Selection of Rationalizability,” Journal
of Economic Theory, 151, 448475 2014.
• Morris, S., and H.S. Shin, “Unique equilibrium in a model of self-fulfilling currency attacks,”
The American Economic Review, 88, 3, 587-597, 1998.
• Angeletos, G.M., C. Hellwig, and A. Pavan, “Signaling in a global game: Coordination and
policy traps,” Journal of Political Economy, 114, 3, 452-484, 2006.
Robustness to Misspecifying the Parameter Set
• Liu, Q., “Representation of belief hierarchies in games with incomplete information,” Journal
of Economic Theory, 2009.
• Ely, J., and M. Peski, “Hierarchies of belief and interim rationalizability,” Theoretical Economics, 1.
• Dekel, E., D. Fudenberg and S. Morris, “Interim Correlated Rationalizability,” Theoretical
Economics, 2, 15-40, 2007.
Other Robustness Questions
• Friedenberg, A., and M. Meier, “The Context of the Game,” Economic Theory, forthcoming.
• Yildiz, M., “Invariance to Representation of Information,” Games and Economic Behavior,
2015.
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4. Incomplete Information: Dynamic Games
Solution Concepts: Perfect Bayesian Equilibrium, Sequential Equilibrium, and Forward Induction
* Fudenberg, D., and J. Tirole, “Perfect Bayesian equilibrium and sequential equilibrium,”
Journal of Economic Theory, 53, 2, 236-260, 1991.
• Battigalli, P., “Strategic Independence and PBE,” Journal of Economic Theory, 1996.
* Watson, J., “Perfect Bayesian Equilibrium: General Definitions and Illustrations,” 2016.
* Kreps, D. and R. Wilson, “Sequential equilibria,” Econometrica, 863–894, 1982.
• Kreps, D. and G. Ramey, “Structural consistency, consistency, and sequential rationality,”
Econometrica, 1331-1348, 1987.
• Cho, I.K., and D.M. Kreps, “Signaling games and stable equilibria,” The Quarterly Journal
of Economics, 102, 2, 179-221, 1987.
• Govindan, S., and R. Wilson, “On forward induction,” Econometrica, 77, 1, 1-28, 2009.
Application: Reputation
* Cripps, M., “Reputation”, The New Palgrave Dictionary of Economics.
* Kreps, D., and R. Wilson, “Reputation and imperfect information,” Journal of Economic
Theory, 27, 253279, 1982.
* Milgrom, P., and J. Roberts, “Predation, reputation and entry deterrence,” Journal of Economic Theory, 27, 280312.
* Mailath, G., and L. Samuelson, Repeated Games and Reputations: Long Run Relationships,
Part IV.
• Hart, S., “Nonzero-sum two-person repeated games with incomplete information,” Mathematics of Operations Research,10,117153, 1985.
• Fudenberg, D. and D. Levine, “Reputation and Equilibrium Selection in Games with a Patient
Player,” Econometrica, 57, 759-778, 1989.
• Mailath, G., and L Samuelson, “Who Wants a Good Reputation?,” Review of Economic
Studies, 68, 415-441, 2001.
* Ely, J., and J. Valimaki, “Bad Reputation,” The Quarterly Journal of Economics, 118, 785-81,
2003.
* Cripps, M., G. Mailath, and L. Samuelson, “Imperfect monitoring and impermanent reputations,” Econometrica, 72, 407432, 2004.
• Board, O., and M. Meyer-Ter-Vehn, “Reputation for Quality,” Econometrica, 81, 23812462,
2013.
• Cripps, M. and E. Faingold, “The Value of a Reputation under Imperfect Monitoring,” 2015.
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5. Bargaining
Complete Information
* Rubinstein, A., “Perfect equilibrium in a bargaining model,” Econometrica, 50, 1, 97-109,
1982.
Private Information
• Fudenberg, D, and J. Tirole, “Sequential bargaining with incomplete information,” The Review of Economic Studies, 50,2, 221-247, 1983.
• Sobel, J., and I. Takahashi, “A multistage model of bargaining,” The Review of Economic
Studies, 50,3, 411-426, 1983.
* Gul, F., H. Sonnenshein, R. Wilson, “Foundations of Dynamic Monopoly and the Coase
Conjecture,” Journal of Economic Theory, 1986.
• Admati, A. R., M. Perry, “Strategic delay in bargaining,” The Review of Economic Studies,
54,3 345-364, 1987.
* Gul, F., and H. Sonnenschein, “On delay in bargaining with one-sided uncertainty.” Econometrica, 601-611, 1988.
• Ausubel, L., and R. Deneckere, “Reputation in bargaining and durable goods monopoly.”
Econometrica, 511-531, 1989.
• Feinberg, Y., and A. Skrzypacz, “Uncertainty about uncertainty and delay in bargaining.”
Econometrica, 73,1, 69-91, 2005.
• Fuchs, W, and A. Skrzypacz, “Bargaining with deadlines and private information.” American
Economic Journal: Microeconomics, 5,4, 219-243, 2013.
Reputational Bargaining
• Myerson, R. Game Theory, Harvard university press, 2013.
• Chatterjee, K., and L. Samuelson, “Bargaining with two-sided incomplete information: An
infinite horizon model with alternating offers.” The Review of Economic Studies, 54, 2, 175192, 1987.
* Abreu, D. F Gul, “Reputational Bargaining,” Econometrica, 68, 85-117, 2000.
• Abreu, D. D. Pearce, “Bargaining, reputation, and equilibrium selection in repeated games
with contracts,” Econometrica, 75, 653-710, 2007.
• Compte, O., and P. Jehiel, “On the role of outside options in bargaining with obstinate
parties.” Econometrica, 70,4, 1477-1517, 2002.
• Wolitzky, A. “Reputational bargaining with minimal knowledge of rationality,” Econometrica,
80, 5, 2047-2087, 2012.
• Abreu, D., D. Pearce, E. Stacchetti. “Onesided uncertainty and delay in reputational bargaining,” Theoretical Economics, 10,3, 719-773, 2015.
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6. Repeated and Stochastic Games
Basic Structure, Modeling Choices, and Perfect Monitoring
* Kandori, M., “Repeated Games,” The New Palgrave Dictionary of Economics.
* Mailath, G., and L. Samuelson, Repeated Games and Reputations: Long Run Relationships,
Part I.
• Blackwell, D., “An analog of the minimax theorem for vector payoffs,” Pacific Journal of
Mathematics, 6, 1, 1-8, 1956.
• Fudenberg, D., and E. Maskin, “The Folk Theorem in Repeated Games with Discounting and
with Incomplete Information,” Econometrica, 54, 533-554, 1986.
• Fudenberg, D., D. Kreps, and E. Maskin, “Repeated Games with Long-Run and Short-Run
Players,” Review of Economic Studies, 57, 1990.
• Lehrer, E., and A. Pauzner, “Repeated games with differential time preferences,” Econometrica, 67, 393-412, 1999.
• Obara, I., and J. Park, “Dynamic Games with General Time Preferences,” 2015.
Imperfect (Public and Private) Monitoring
* Mailath, G., and L. Samuelson, Repeated Games and Reputations: Long Run Relationships,
Part II-III.
* Green, E., and R. Porter, “Noncooperative collusion under imperfect price information,”
Econometrica, 87-100, 1984.
* Fudenberg, D., D. Levine, and E. Maskin, “The Folk Theorem with Imperfect Public Information,” Econometrica, 62, 997-1040, 1986.
* Fudenberg, D. and D. Levine, “Efficiency and Observability with Long-Run and Short-Run
Players,” Journal of Economic Theory, 62, 103-135, 1994.
* Abreu, D., D. Pearce, and E. Stacchetti, “Toward a theory of discounted repeated games with
imperfect monitoring,” Econometrica, 1041-1063, 1990.
• Ely, J., and J. Valimaki, “A Robust Folk Theorem for the Prisoner’s Dilemma,” Journal of
Economic Theory, 102, 84-105, 2002.
• Hörner, J., and W. Olszewski, “The folk theorem for games with private almost-perfect
monitoring,” Econometrica, 74, 6, 2006.
• Sugaya, T., “Folk Theorem in Repeated Games with Private Monitoring,” 2011.
• Yamamoto, Y., “Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under Conditional Independence,” Journal of Economic Theory, 147, 1998-2027, 2012.
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Stochastic Games
• Hörner, J., Sugaya, T., Takahashi, S., and Vieille, N., “Recursive Methods in Discounted
Stochastic Games: An Algorithm for δ → 1 and a Folk Theorem,” Econometrica, 79,
12771318, 2011.
• Hörner, J., Takahashi, S., and Vieille, N., “Truthful Equilibria in Dynamic Bayesian Games.”
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