Perturbation theory for games in normal form and stochastic games

In this paper, the effect on values and optimal strategies of perturbations of game parameters (payoff function, transition probability function, and discount factor) is studied for the class of zero-sum games in normal form and for the class of stationary, discounted, two-person, zero-sum stochastic games.A main result is that, under certain conditions, the value depends on these parameters in a pointwise Lipschitz continuous way and that the sets of -optimal strategies for both players are upper semicontinuous multifunctions of the game parameters.Extensions to general-sum games and nonstationary stochastic games are also indicated.