Game Theory I (A1, 2023)

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

In this course, we study advanced topics on incomplete information games, in particular on information design. Half of the course will consist of lectures by the instructor and the other half of presentations by students.
Students are encouraged to take the following math courses:

• Mathematics for Economics (S; Prof. Matsui) or Mathematics II (S1)
• Mathematical Economics (S2)
• Probability Theory and Applications to Economic Theory (S; Prof. Satoru Takahashi)

Readings

Correlated equilibrium

• Aumann, R.J. (1974). ``Subjectivity and Correlation in Randomized Strategies,'' Journal of Mathematical Economics 1, 67-96.
• 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.

Bayes correlated equilibrium/Partial implementation

• *Bergemann, D. and S. Morris (2016). ``Bayes Correlated Equilibrium and the Comparison of Information Structures in Games,'' Theoretical Economics 11, 487-522.
• Taneva, I. (2019). ``Information Design,'' American Economic Journal: Microeconomics 11, 151-185.
• *Bergemann, D. and S. Morris (2019). ``Information Design: A Unified Perspective,'' Journal of Economic Literature 57, 44-95.
• Arieli, I. and Y. Babichenko (2019). ``Private Bayesian Persuasion,'' Journal of Economic Theory 182, 185-217.

Email game, global games/Full implementation with payoff perturbations

• *Rubinstein, A. (1989). ``The Electronic Mail Game: Strategic Behavior under `Almost Common Knowledge','' American Economic Review 79, 385-391.
• Carlsson, H. and E. van Damme (1993). ``Global Games and Equilibrium Selection,'' Econometrica 61, 989-1018.
• 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 (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]
• Morris, S. and H. S. Shin (2007). ``Common Belief Foundations of Global Games.''
• Morris, S., H. S. Shin, and M. Yildiz (2016). ``Common Belief Foundations of Global Games,'' Journal of Economic Theory 163, 826-848.
• Basteck, C., T. R. Daniels, and F. Heinemann (2010). ``Characterising Equilibrium Selection in Global Games with Strategic Complementarities,'' SFB 649 Discussion Paper 2010-008, Humboldt University.
• Basteck, C., T. R. Daniels, and F. Heinemann (2013). ``Characterising Equilibrium Selection in Global Games with Strategic Complementarities,'' Journal of Economic Theory 48, 2620-2637.
• Iijima, R. (2015). ``Iterated Generalized Half-Dominance and Global Game Selection,'' Journal of Economic Theory 159, 120-136.
• Morris, S., D. Oyama, and S. Takahashi (2023). ``Global Game Selections in Binary-Action Supermodular Games.''

Robustness to incomplete information

• *Kajii, A. and S. Morris (1997). ``The Robustness of Equilibria to Incomplete Information,'' Econometrica 65, 1283-1309.
• *Kajii, A. and S. Morris (2020). ``Refinements and Higher Order Beliefs: A Unified Survey,'' Japanese Economic Review 71, 7-34.
• Kajii, A. and S. Morris (2020). ``Notes on ``Refinements and Higher Order Beliefs: A Unified Survey'','' Japanese Economic Review 71, 35-41.
• 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.
• Haimanko, O. and A. Kajii (2016). ``Approximate Robustness of Equilibrium to Incomplete Information,'' International Journal of Game Theory 45,839-857.
• 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.
• Oyama, D. and O. Tercieux (2012). ``On the Strategic Impact of an Event under Non-Common Priors,'' Games and Economic Behavior 74, 321-331.
• 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.
• *Oyama, D. and S. Takahashi (2019). ``Generalized Belief Operator and the Impact of Small Probability Events on Higher Order Beliefs.''
• *Oyama, D. and S. Takahashi (2020). ``Generalized Belief Operator and Robustness in Binary-Action Supermodular Games,'' Econometrica 88, 693-726.
• Morris, S. and T. Ui (2020). ``Incomplete Information Robustness.''
• *Oyama, D. and S. Takahashi (2023). ``Robustness in Binary-Action Supermodular Games Revisited.''
• *Morris, S., D. Oyama, and S. Takahashi (2023). ``Strict Robustness to Incomplete Information,'' Japanese Economic Review 74, 357-376.

Smallest equilibrium implementation, full implementation

• Kamien, M. I., Y. Tauman, and S. Zamir (1990). ``On the Value of Information in a Strategic Conflict,'' Games and Economic Behavior 2, 129-153.
• Bergemann, D. and S. Morris (2019). Section 7.1.
• Carroll, G. (2016). ``Informationally Robust Trade and Limits to Contagion,'' Journal of Economic Theory 166, 334-361.
• Mathevet, L., L. Perego, and I. Taneva (2020). ``On Information Design in Games,'' Journal of Political Economy 128, 1370-1404.
• Hoshino, T. (2022). ``Multi-Agent Persuasion: Leveraging Strategic Uncertainty,'' International Economic Review 63, 755-776.
• Inostroza N. and A. Pavan (2023). ``Adversarial Coordination and Public Information Design.''
• Li, F., Y. Song, and M. Zhao (2023). ``Global Manipulation by Local Obfuscation,'' Journal of Economic Theory 207, 105575.
• *Morris, S., D. Oyama, and S. Takahashi (2020). ``Implementation via Information Design in Binary-Action Supermodular Games.''
• *Morris, S., D. Oyama, and S. Takahashi (2022). ``Implementation via Information Design using Global Games.''

Applications

• Sakovics, J. and J. Steiner (2012). ``Who Matters in Coordination Problems?'' American Economic Review 102, 3439-3461.
• Moriya, F. and T. Yamashita (2020). ``Asymmetric-Information Allocation to Avoid Coordination Failure,'' Journal of Economics & Management Strategy 29, 173-186.
• *Halac, M., E. Lipnowski, and D. Rappoport (2021). ``Rank Uncertainty in Organizations,'' American Economic Review 111, 757-86.
• *Morris, S., D. Oyama, and S. Takahashi (2022). ``On the Joint Design of Information and Transfers.''

Other related papers

• Bergemann, D., B. Brooks, and S. Morris (2015). ``The Limits of Price Discrimination,'' American Economic Review.
• Bergemann, D., B. Brooks, and S. Morris (2022). ``Counterfactuals with Latent Information,'' American Economic Review.
• Doval, L. and J. Ely (2020). ``Sequential Information Design,'' Econometrica.
• Gossner, O. and R. Veiel (2022). ``Rationalizable Outcome Distributions: A Markov Characterization.''
• Pei, H. and B. Strulovici (2023). ``Robust Implementation with Costly Information.''
• Sato, H. (2023). ``Robust Implementation in Sequential Information Design under Supermodular Payoffs and Objective,'' Review of Economic Design 27, 269-285.

Topics

• Introduction (10/5)
• Correlated Equilibrium (10/5)
• Bayes Correlated Equilibrium (10/9)
• Email Game (10/12)
• Global Games I (10/12)
• Robustness to Incomplete Information (10/16)
• Robustness in Binary-Action Supermodular Games (10/19, 10/23)
• Smallest Equilibrium Implementation in Binary-Action Supermodular Games (10/26, 10/30)
• Smallest Equilibrium Implementation by Global Games (10/30)
• Full Implementation in Binary-Action Supermodular Games (11/1)
• Robustness and Information Design (11/1)
• Joint Design of Information and Transfers (11/2)

Student presentations

Office hours