Topics in Game Theory

We will cover solution concepts (two weeks), the universal type space (one week), approximate common knowledge (two weeks), strategic topologies (three weeks), robustness to incomplete information (three weeks), and informationally robust mechanism design (two weeks).

Lectures and students' presentations

Participation, presentation, and homework.

N/A

Papers with * will be covered in the class: 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. Ely, J. and M. Peski (2006). ``Hierarchies of Belief and Interim Rationalizability,'' Theoretical Economics 1, 19-65. *Dekel, E., D. Fudenberg, and S. Morris (2007). ``Interim Correlated Rationalizability,'' Theoretical Economics 2, 15-40. *Bergemann, D. and S. Morris (2016). ``Bayes Correlated Equilibrium and the Comparison of Information Structures in Games,'' Theoretical Economics 11, 487–522 The 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. 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) Carlsson, H. and E. van Damme (1993). ``Global Games and Equilibrium Selection,'' Econometrica 61, 989-1018. Morris, S. (1999). ``Approximate Common Knowledge Revisited,'' International Journal of Game Theory 28, 385-408. Takahashi, S. and O. Tercieux (2020). ``Robust Equilibrium Outcomes in Sequential Games under Almost Common Certainty of Payoffs.'' Journal of Economic Theory 188, 105068. Strategic Topologies *Dekel, E., D. Fudenberg, and S. Morris (2006). ``Topologies on types,'' Theoretical Economics 1, 275-309. *Weinstein, J. and M. Yildiz (2007). ``A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements,'' Econometrica 75, 365-400. Chen, Y.-C., A. Di Tillio, E. Faingold, and S. Xiong (2010). ``Uniform Topologies on Types,'' Theoretical Economics 5 (2010), 445-478. Ely, J. and M. Peski (2011). ``Critical Types,'' Review of Economic Studies 78, 907-937. Chen, Y.-C., A. Di Tillio, E. Faingold, and S. Xiong (2017). ``Characterizing the Strategic Impact of Misspecified Beliefs,'' Review of Economic Studies 84, 1424-1471. Chen, Y.-C., S. Takahashi, and S. Xiong (2022). ``Robust Refinement of Rationalizability.'' 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 (1997). ``The Robustness of Equilibria to Incomplete Information,'' Econometrica 65, 1283-1309. 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. Takahashi, S. (2020). ``Non-Equivalence between All and Canonical Elaborations,'' Japanese Economic Review 71, 43-57. *Oyama, D. and S. Takahashi (2020). ``Generalized Belief Operator and the Impact of Small Probability Events on Higher Order Beliefs.'' Econometrica 88, 693-726. *Morris, S., D. Oyama, and S. Takahashi (2022). ``Implementation via Information Design in Binary-Action Supermodular Games.'' Informationally Robust Mechanism Design: TBA

N/A