  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.
