The game for the speed of convergence in repeated games of incomplete information

Abstract

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) in- formed player. Such games have value vyð pÞ for all 0 a p a 1. The informed player can guarantee that all along the game the average payoper stage will be greater than or equal to vyðpÞ (and will converge from above to vyðpÞ if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payos-to the value vyð pÞ. In the context of such repeated games, we define a game for the speed of convergence, denoted SGyðpÞ, and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which vnðpÞ� vyðpÞ is of the order of magnitude of 1ffiffi