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 r1, r2, ∈ N, where N also represents the set of stages of the game. If, at any stage τ, player k ∈ {1, 2} did not select action i at any of the preceding rk stages, then action i will vanish from his set of actions and will no longer be available in the remaining play. For several (r1, r2)-cases we show the existence of optimal strategies for limiting average optimal play