具有转换成本的重复博弈：平稳策略与历史独立策略
Repeated Games with Switching Costs: Stationary vs History Independent Strategies
摘要：
我们研究的零和重复博弈中，最小化的球员必须支付一定的成本，每次他改变他的行动。我们的贡献是双重的。首先，我们证明了博弈的价值存在于静态策略中，仅取决于最小化参与者的先前行动，而不是整个历史。我们提供了一个完整的表征的价值和最优策略。该策略表现出鲁棒性，通常不会改变一个小扰动的切换成本。其次，我们考虑一种情况下，最小化的球员是有限的发挥简单的策略，是完全独立的历史。在这里，我们也提供了一个完整的（极大极小）值和获得它的策略的特征。此外，我们提出了几个界限的损失，由于这种限制。
英文摘要：
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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