Dynamical Analysis of a Repeated Game with Incomplete Information

We study a two player repeated zero-sum game with asymmetric information introduced by Renault in which the underlying state of the game undergoes Markov evolution (parameterized by a transition probability, p, in the range 12 to 1). Horner, Rosenberg, Solan and Vieille identified an optimal strategy, sigma* for the informed player for p in the range [1/2, 2/3]. We extend the range on which sigma* is proved to be optimal to about [1/2, 0.719] and prove that it fails to be optimal at a value around 0.7328. Our techniques make use of tools from dynamical systems, specifically the notion of pressure, introduced by D. Ruelle.