Continuous-time stochastic games

We study continuous-time stochastic games, 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 and that the discounting game and the more general game with time-separable payoffs have an epsilon equilibrium that is an epsilon equilibrium in all 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 and a mass at infinity. 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.