We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, which depend solely on the previous action of the player (and not the entire history ), and we provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the  player is limited to playing  completely history-independent strategies and provide a full characterization of the value and optimal strategies in this case. Naturally, this limitation worsens his situation. We deduce a bound on his loss in the general case as well as more precise bounds when more assumptions regarding the game or the switching costs are introduced .
We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history . We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent . Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation .
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value and optimal strategies in this case. Naturally, this limitation worsens his situation. We deduce a bound on his loss in the general case as well as more precise bounds when more assumptions regarding the game or the switching costs are introduced
(minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation