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In repeated games with incomplete information, rational agents must carefully weigh the tradeoffs of advantageously exploiting their information to achieve a short-term gain versus carefully concealing their information so as not to give up a long-term informed advantage. The theory of infinitely-repeated two-player zero-sum games with incomplete information has been carefully studied, beginning with the seminal work of Aumann and Maschler. While this theoretical work has produced a characterization of optimal strategies, algorithms for solving for optimal strategies have not yet been studied. For the case where one player is informed about the true state of the world and the other player is uninformed, we provide a non-convex mathematical programming formulation for computing the value of the game, as well as optimal strategies for the informed player. We then describe an efficient algorithm for solving this difficult optimization problem to within arbitrary accuracy. We also discuss how to efficiently compute optimal strategies for the uninformed player using the output of our algorithm.

Solving two-person zero-sum repeated games of incomplete information