On finite strategy sets for finitely repeated zero-sum games. (Q1399527)

The authors consider a finitely repeated two-person zero-sum game \(G_K^N\), in which Player 1 is restricted to picking a set of \(K\) pure strategies and then mixing over these strategies. \(N\) is number of stages. Player 2 is not restricted in the choice. They show that Player 1 can play optimally by choosing a set of pure strategies that ignore Player's 2 actions. Follow by [\textit{A. Neyman} and \textit{D. Okada}, ``Strategic entropy and complexity in repeated games'', Games Econ. Behav. 29, 191--223 (1999; Zbl 1002.91004)] they introduce strategic entropy and use it to derive the upper and lower bounds on the value of repeated games.