Robustness to Incomplete Information in Repeated and Dynamic Games

This paper extends Kajii and Morris (1997)’s notion of robustness to incomplete information to repeated and more generally dynamic games. We argue that in dynamic games, the requirements of robustness should be strengthened to allow for small payoff deviations with large probability. Under this strengthening, we show that dynamically robust equilibria can be characterized by applying a one-shot robustness principle that extends the one-shot deviation principle. For repeated games, this implies a factorization result analogous to that of Abreu, Pearce and Stacchetti (1990). We then apply these results to characterize explicitly the set of robust equilibria in the repeated Prisoners’ Dilemma and show that cooperation is robustly sustainable if and only if both (Cooperate,Cooperate) and (Cooperate,Defect) are enforceable under complete information. Robustness considerations also nuance our analysis of the repeated Prisoners’ Dilemma in interesting ways. In particular, grim-trigger strategies may be less robust than asymmetric strategies which do not punish both players upon unilateral deviation. ∗[email protected] †[email protected]