Private information in repeated games

This dissertation studies private information in repeated games with imperfect monitoring. For this class of repeated games, it is typically assumed that all agents/players share the same information or use only such common information. Although this restriction makes analysis simple and tractable, it is natural to think that there are situations where agents/players can obtain some useful private information through their long-term relationships. The goal of this research is to identify possible roles of private information in long-term relationships. The first chapter (joint with Michihiro Kandori) focuses on private information endogenously generated during the game; players' own past actions. We construct a sequential equilibrium using private strategies: strategies that depend on chosen actions as well as observed public signals. Our main finding is that players can sometimes make better use of information by using private strategies, and efficiency in repeated games can often be drastically improved. The rest of the dissertation consider repeated games with only private signals, which are called repeated games with private monitoring. The second chapter (joint with Venkataraman Bhaskar) explores the possibility of folk theorem for such games, focusing in particular on the efficient outcome. We study infinitely repeated prisoners' dilemma games with almost perfect private monitoring. We show that the symmetric efficient outcome can be approximated in any prisoners' dilemma game, while every individually rational feasible payoff can be approximated in a class of prisoners' dilemma games. We also extend the approximate efficiency result to n-player prisoners' dilemma games. The last chapter (joint with Richard McLean and Andrew Postlewaite) addresses a different issue; robustness of perfect public equilibrium. Monitoring is still private, but players can communicate each period. We fix an arbitrary equilibrium with public monitoring and investigate the possibility of approximating the particular equilibrium in the private monitoring setting which is “close” to the original public monitoring setting. We identify a sufficient condition on the private monitoring structure such that uniformly strict perfect public equilibria are robust.