Bayesian Repeated Zero-Sum Games with Persistent State, with Application to Security Games

We study infinitely-repeated two-player zero-sum games with one-sided private information and a persistent state. Here, only one of the two players learns the state of the repeated game. We consider two models: either the state is chosen by nature, or by one of the players. For the former, the equilibrium of the repeated game is known to be equivalent to that of a one-shot public signaling game, and we make this equivalence algorithmic. For the latter, we show equivalence to one-shot team max-min games, and also provide an algorithmic reduction. We apply this framework to repeated zero-sum security games with private information on the side of the defender and provide an almost complete characterization of their computational complexity.

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