Player type distributions as state variables and information relevation in zero sum repeated games with discounting

This paper examines the role of the player type distributions in repeated zero sum games of incomplete information with discounting of payoffs. In particular the strategic ‘sufficiency’ of the posterior distributions for histories and the limiting properties of the posterior sequence are discussed. It is shown that differentiability of the value function is sufficient to allow the posteriors to serve as ‘state’ variables for histories. The limiting properties of the posterior distributions are considered and a characterization given of the set of possible limit points of the posterior distribution. This characterization is given in terms of the ‘value’ of information in the one-stage game.