Uniform Equilibrium: More than Two Players

Abstract

The basic question addressed in this chapter is: Does every multi-player stochastic game (with finite state and action spaces) admit a uniform equilibrium payoff? To this day, no counterexample has been found. A positive answer has been given for several special classes, including zero-sum stochastic games [9], two-player non-zero-sum absorbing games [28] and two-player non-zero-sum stochastic games [26]. For multi-player games, existence of stationary equilibrium profiles has been proven for irreducible games [14],[3] and of “almost” stationary equilibrium profiles for games with additive rewards and additive transitions as well as for games with perfect information [25]. In this chapter I review recent results for games with more than two players.