Repeated Games with Bounded Entropy

We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of the maximizer’s strategies while the other player is unrestricted. We will show that if the Ž . bound h n , a function of the number of repetitions n, satisfies the condition Ž . Ž . nŽ Ž .. Ž .Ž . h n rn a g n a ` , then the maxmin value W h n converges to cav U g , the concavification of the maxmin value of the stage game in which the maximizer’s actions are restricted to those with entropy at most g . A similar result is obtained for the infinitely repeated games. Journal of Economic Literature Classification Numbers: C73, C72. Q 2000 Academic Press