Continuous-time stochastic games

We study continuous-time stochastic games (with finitely many states and actions), with a focus on the existence of their equilibria that are insensitive to a small imprecision in the specification of players’ evaluations of streams of payoffs. We show that the stationary, namely, time-independent, discounting game has a stationary equilibrium, that the (not necessarily stationary) discounting game and the more general game with time separable payoffs (where the discounting or time-separable payoffs can vary among the players) has an epsilon equilibrium, and that in all the above-mentioned cases there are strategy profiles that are epsilon equilibrium in all the games with a sufficiently small perturbation of the players’ valuations. A limit point of discounting valuations need not be a discounting valuation as some of the “mass” may be pushed to infinity; it is represented by an average of a discounting valuation (which represents the impatient part of the valuation) and a mass at infinity (which represents the patient part of the valuation). We show that for every such limit point there is a strategy profile that is an epsilon equilibrium of all the discounting games with discounting valuations that are sufficiently close to the limit point. ∗Institute of Mathematics, and the Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. E-mail: [email protected] This research was supported in part by Israel Science Foundation grant 1596/10.