Unlearning by not doing: Repeated games with vanishing actions

We examine two-person zero-sum repeated games in which the players' action choices are restricted in the following way. Let r(1), r2 epsilon N, where N also represents the set of stages of the game. If, at any stage tau, player epsilon {1, 2} did not select action i at any of the preceding r(k) stages, then action i will vanish from his set of actions and will no longer be available in the remaining play. For several (r(1), r(2))-cases we show the existence of optimal strategies for limiting average optimal play. Journal of Economic Literature Classification Numbers: C72, C73.