  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.
