The Regularity of the Value Function of Repeated Games with Switching Costs

We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. derive properties value and optimal strategies as function ratio between switching costs stage payoffs. In particular, exhibit robustness property typically do not change with small perturbation this ratio. Our analysis extends partially to case are limited simpler that history independent―namely, static strategies. case, we also characterize (minimax) for obtaining it.