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.
|Publisher||Cornell University - arXiv|
|Number of pages||40|
|Publication status||Published - 26 Feb 2021|
- c72 - Noncooperative Games
- c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"
- switching costs
- repeated games
- stochastic games
- zero-sum games