Abstract:

We study the repeated games with a bound on strategic entropy (Neyman and Okada (1996)) of player 1's strategy while player 2's strategy is unrestricted. The strategic entropy bound will be a function (N) of the number of repetitions N, and hence, so is the maximin value of N((N)) of the repeated game with such bound. Our interest is in the asymptotic behavior of N((N)) (as N ) under the condition the per stage entropy bound, (N)/N where 0. We characterize the asymptotics of N((N)) by a continuous function of . Specifically, it is shown that this function is the concavification of the maximin value of the stage game in which player 1's action is restricted to those with entropy at most . We also show that, for infinitely repeated games, if player 1's strategies are restricted to those with strategic entropy rate at most , then the maximin value () exists and it, too, equals the concavified function mentioned above evaluated at .

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