Topics in Economic Theory (A1, 2015)

OYAMA Daisuke
oyama@e.u-tokyo.ac.jp

In this course, we study advanced topics on incomplete information games and network games. Half of the course will consist of lectures by the instructor and the other half of presentations by the students.

Topics include:

• solution concepts;
• universal type space;
• contagion and robustness in incomplete information games;
• contagion and uninvadability in network games.

Readings

Solution Concepts

• Aumann, R.J. (1974). ``Subjectivity and Correlation in Randomized Strategies,'' Journal of Mathematical Economics 1, 67-96. 
• Bernheim, D. (1984). ``Rationalizable Strategic Behavior,'' Econometrica 52, 1007-1028. 
• Pearce, D. (1984). ``Rationalizable Strategic Behavior and the Problem of Perfection,'' Econometrica 52, 1029-1050.
• Aumann, R.J. (1987). ``Correlated Equilibrium as an Expression of Bayesian Rationality,'' Econometrica 55, 1-28. 
• *Brandenburger, A. and E. Dekel (1987). ``Rationalizability and Correlated Equilibria,'' Econometrica 55, 1391-1402. (9/11)
• *Dekel, E., D. Fudenberg, and S. Morris (2007). ``Interim Correlated Rationalizability,'' Theoretical Economics 2, 15-40. (9/18)
• **Bergemann, D. and S. Morris (2015). ``Bayes Correlated Equilibrium and the Comparison of Information Structures in Games,'' forthcoming in Theoretical Economics. (Nakada 10/13)

Common Prior Assumption

• Aumann, R.J. (1976). ``Agreeing to Disagree,'' Annals of Statistics 4, 1236-1239.
• Samet, D. (1998). ``Iterated Expectations and Common Priors,'' Games and Economic Behavior 24, 131-141.
• Samet, D. (1998). ``Common Priors and the Separation of Convex Sets,'' Games and Economic Behavior 24, 172-174
• *Lipman, B.L. (2003). ``Finite Order Implications of Common Priors,'' Econometrica 71, 1255-1267. [Supplemental Notes] (9/22)
• *Lipman, B.L. (2010). ``Finite Order Implications of Common Priors in Infinite Models,'' Journal of Mathematical Economics 46, 56-70. (9/22)

Universal Type Space

• Mertens, J.-F. and S. Zamir (1985). ``Formulation of Bayesian Analysis for Games with Incomplete Information,'' International Journal of Game Theory 14, 1-29.
• *Brandenburger, A. and E. Dekel (1993). ``Hierarchies of Beliefs and Common Knowledge,'' Journal of Economic Theory 59, 189-198. (9/14)
• Heifetz, A. and D. Samet (1998). ``Topology-Free Typology of Beliefs,'' Journal of Economic Theory 82, 324-341.

Approximate Common Knowledge

• Rubinstein, A. (1989). ``The Electronic Mail Game: Strategic Behavior under `Almost Common Knowledge','' American Economic Review 79, 385-391.
• *Monderer, D. and D. Samet (1989). ``Approximating Common Knowledge with Common Beliefs,'' Games and Economic Behavior 1, 170-190. (9/25)
• Morris, S. (1999). ``Approximate Common Knowledge Revisited,'' International Journal of Game Theory 28, 385-408.

Robustness to Incomplete Information

• Morris, S., R. Rob, H.S. Shin (1995). ``p-Dominance and Belief Potential,'' Econometrica 63, 145-157.
• *Kajii, A. and S. Morris (1997a). ``The Robustness of Equilibria to Incomplete Information,'' Econometrica 65, 1283-1309. (9/29)
• *Kajii, A. and S. Morris (1997b). ``Refinements and Higher Order Beliefs: A Unified Survey.'' [Download] (9/25, 29)
• Ui, T. (2001). ``Robust Equilibria of Potential Games,'' Econometrica 69, 1373-1380.
• Morris, S. and T. Ui (2005). ``Generalized Potentials and Robust Sets of Equilibria,'' Journal of Economic Theory 124, 45-78.
• *Weinstein, J. and M. Yildiz (2007). ``A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements,'' Econometrica 75, 365-400. (9/22)
• Oyama, D. and O. Tercieux (2009). ``Iterated Potential and Robustness of Equilibria,'' Journal of Economic Theory 144, 1726-1769.
• *Oyama, D. and O. Tercieux (2010). ``Robust Equilibria under Non-Common Priors,'' Journal of Economic Theory 145, 752-784. (10/6)
• *Oyama, D. and O. Tercieux (2012). ``On the Strategic Impact of an Event under Non-Common Priors,'' Games and Economic Behavior 74, 321-331. (10/6)
• *Oyama, D. and S. Takahashi (2015). ``Generalized Belief Operator and the Impact of Small Probability Events on Higher Order Beliefs.'' (10/2)

Global Games

• Carlsson, H. and E. van Damme (1993). ``Global Games and Equilibrium Selection,'' Econometrica 61, 989-1018.
• Kim, Y. (1996). ``Equilibrium Selection in n-Person Coordination Games,'' Games and Economic Behavior 15, 203-227.
• Frankel, D., S. Morris, and A. Pauzner (2003). ``Equilibrium Selection in Global Games with Strategic Complementarities,'' Journal of Economic Theory 108, 1-44.
• Morris, S. and H. S. Shin (1998). ``Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks,'' American Economic Review 88, 587-597.
• Morris, S. and H. S. Shin (2003). ``Global Games: Theory and Applications,'' in M. Dewatripont, L. P. Hansen, and S. J. Turnovsky, eds., Advances in Economics and Econometrics: Theory and Applications: Eighth World Congress, Volume 1, Cambridge University Press: Cambridge. [download]
• Basteck, C. and T. R. Daniels (2011). ``Every Symmetric 3 × 3 Global Game of Strategic Complementarities Has Noise-Independent Selection,'' Journal of Mathematical Economics 47, 749-754.
• Honda, J. (2011). ``Noise-Independent Selection in Global Games and Monotone Potential Maximizer: A Symmetric 3 × 3 Example,'' Journal of Mathematical Economics 47, 663-669.
• Oyama, D. and S. Takahashi (2011). ``On the Relationship between Robustness to Incomplete Information and Noise-Independent Selection in Global Games,'' Journal of Mathematical Economics 47, 683-688.
• Morris, S. and H. S. Shin (2007). ``Common Belief Foundations of Global Games.''
• **Morris, S., H. S. Shin, and M. Yildiz (2015). ``Common Belief Foundations of Global Games.'' (Tsukada 10/9)

Interaction Games

• Morris, S. (1997). ``Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching.''
• Morris, S. (1999). ``Potential Methods in Interaction Games.''
• **Morris, S. (2000). ``Contagion,'' Review of Economic Studies 67, 57-78. (Sakai 10/16)
• Morris, S. and H. S. Shin (2005). ``Heterogeneity and Uniqueness in Interaction Games.''
• Mailath, G. J., L. Samuelson, A. Shaked (1997). ``Correlated Equilibria and Local Interactions,'' Economic Theory 9, 551-556.
• Oyama, D. and S. Takahashi (2015). ``Contagion and Uninvadability in Local Interaction Games: The Bilingual Game and General Supermodular Games,'' Journal of Economic Theory 157, 100-127 .
• Oyama, D., S. Takahashi, and J. Hofbauer (2008). ``Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics,'' Theoretical Economics 3, 155-192.
• Takahashi, S. (2008). ``Perfect Foresight Dynamics in Games with Linear Incentives and Time Symmetry,'' International Journal of Game Theory 37, 15-38.
• Morris, S. (2014). ``Coordination, Timing and Common Knowledge,'' Research in Economics 68, 306-314.
• **Galeotti, A., S. Goyal, M.O. Jackson, F. Vega-Redondo, and L. Yariv (2010). ``Network Games,'' Review of Economic Studies 77, 218-244. (Nakayama 10/20)
• **Golub, B. and M.O. Jackson (2012). ``How Homophily Affects the Speed of Learning and Best-Response Dynamics,'' Quarterly Journal of Economics 127, 1287-1338. (Hashidate 10/23)

Slides

• Rationalizability and Correlated Equilibria (9/11)
• Hierarchies of Beliefs and Common Knowledge (9/15)
• Interim Correlated Rationalizability (9/18)
• Properties of the Product Topology on the Universal Type Space (9/21)
• Approximating Common Knowledge with Common Beliefs (9/25)
• The Robustness of Equilibria to Incomplete Information (9/29)
• Generalized Belief Operator and the Impact of Small Probability Events on Higher Order Beliefs (10/2)
• On the Strategic Impact of an Event under Non-Common Priors (10/5)
• Robust Equilibria under Non-Common Priors (10/5)

Office hours