Repeated Games with Bounded Entropy

Abstract 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 bound η( n ), a function of the number of repetitions n , satisfies the condition η( n )/ n  → γ ( n  → ∞), then the maxmin value W n (η( n )) converges to (cav  U )(γ), the concavification of the maxmin value of the stage game in which the maximizer's actions are restricted to those with entropy at most γ. A similar result is obtained for the infinitely repeated games. Journal of Economic Literature Classification Numbers: C73, C72.