Codes of conduct, private information and repeated games

We examine self-referential games in which there is a chance of understanding an opponent’s intentions. Our main focus is on the interaction of two sources of information about opponents’ play: direct observation of the opponent’s code-of-conduct, and indirect observation of the opponent’s play in a repeated setting. Using both sources of information we are able to prove a “folk-like” theorem for repeated self-referential games with private information. This theorem holds even when both sources of information are weak. 1 The idea of self-referential equilibrium was developed in an earlier collaboration between Levine and Wolfgang Pesendorfer and the ideas about approximate equilibrium and private information with Drew Fudenberg. Levine is especially grateful to them, as well as to Phillip Johnson, Balazs Szentes and George Mailath for the many discussions that motivated this work. We also thank Satoru Takahashi for helpful comments. National Science Foundation (Grant SES-0851315) and the European University Institute provided financial support. 2 Ph.D. Candidate, Washington University in St. Louis and John H. Biggs Distinguished Professor, Department of Economics, Washington University in St. Louis, http://www.dklevine.com, [email protected].