Robustness to Incomplete Information in Repeated Games∗

This paper extends the framework of Kajii and Morris (1997) to study the question of robustness to incomplete information in repeated games. We show that dynamically robust equilibria can be characterized using a one-shot robustness principle that extends the one-shot deviation principle. Using this result, we compute explicitly the set of dynamically robust equilibrium values in the repeated prisoners’ dilemma. We show that robustness requirements have sharp intuitive implications regarding when cooperation can be sustained, what strategies are best suited to sustain cooperation, and how changes in payoffs affect the sustainability of cooperation. We also show that a folk theorem in dynamically robust equilibria holds, but requires stronger identifiability conditions than the pairwise full rank condition of Fudenberg, Levine and Maskin (1994). ∗We are particularly grateful to Drew Fudenberg, Stephen Morris, Larry Samuelson and Olivier Tercieux for comments and advice. We thank Dilip Abreu, Eduardo Faingold, Roger Guesnerie, Johannes Hörner, George Mailath, Marcin P ↪ eski, Wolfgang Pesendorfer, Phil Reny, Yuliy Sannikov, Hugo Sonnenschein, Muhamet Yildiz as well as seminar participants at Duke, Johns Hopkins, Paris School of Economics, Penn State, Princeton, Rochester, Rutgers, Toronto, UT Austin, the University of Chicago, the University of Pennsylvania as well as the GRIPS International Workshop, the conference the 2008 Stony Brook Game Theory Festival, and the 2nd Singapore Economic Theory Annual Workshop for helpful conversations. Paul Scott and Takuo Sugaya provided excellent research assistance. Chassang: [email protected], Takahashi: [email protected].