Ex-post regret heuristics under private values (II): 2×2 games

When information is hardly available, the role of priors should be limited in robust game-theoretic predictions. We analyze a process of heuristics based on ex-post regret as a guide to understand how to play games of incomplete information with private values. While our dynamics has a strong component of inertia, its key is that with a small probability actions are modified in the direction of ex-post regrets. We apply stochastic stability to identify the strategies that will be used in the long run in 2×2 games (i.e., two players with two actions each). For a class of 2×2 games, which includes quasi-supermodular games satisfying “weak dominance”, the resulting theory predicts cautious behavior in the long run, as stochastically stable strategies are minimax regret equilibria. A minimax regret equilibrium is independent of the beliefs about the opponents' types and actions (only the supports matter) and suggests a “safe way to play the game”.