Repeated Games with Incomplete Information

Abstract

This chapter presents results on infinitely repeated games with incomplete information. These are nonzero-sum games with lack of information on one side and standard signaling matrices and zero-sum games with more delicate information and signaling patterns. The motivation for games with incomplete information is clear: The most interesting features of social and economic situations are justified by the asymmetry of the information of the individuals involved. The duration of the relationships between agents explains also many parts of behavior, like threat, punishment, reward, careful revelation of knowledge, and patient gathering of information. The model of repeated games has been conceived to study all these aspects related to durable relationships. Under complete information, the main theme is that repetition enables cooperation (Folk Theorem). Under incomplete information, the repetition of the game appears also as a signaling mechanism with all the complexities required by the strategic transmission of information. Discovering the zero-sum case as a necessary step for the nonzero-sum one is not only useful to evaluate minmax levels but also to study under laboratory conditions the artfulness of information exchange. It also focuses on two results on nonzero-sum games, one on Nash equilibria and the other on correlated equilibria.