Strategic transmission of information and repeated game balances.

Summary Modeling a strategic interaction requires paying particular attention to the knowledge that the players have of the situation in which they are participating. In case of repeated interaction, this knowledge is bound to evolve over time. This thesis focuses on the strategic aspects of the evolution of this information. It contains five chapters. The first two chapters concern the existence of uniform equilibria of repeated games with a lack of information on one side (introduced by Aumann and Maschler). The main problem is then to determine how much information can be transmitted to the equilibrium. The existence of equilibria is obtained in some cases, thanks to proofs of convex analysis and the use of statistical techniques. We then study strategic ways of transmitting information, in the sense that they are robust to deviations on the part of a single player. The third chapter introduces a class of repeated games called proximity games, and essentially solves the problem of the defection of a deviation occurring during the game. Finally, the last two chapters are devoted to the possibility of transmitting strategically, deterministically or probabilistically, an information concerning the initial situation of an interaction. Characterizations are given, and links with the existence of fully revealing equilibria in repeated games with incomplete information are shown.