A Discounted Stochastic Game with No Stationary Equilibria: The Case of Absolutely Continuous Transitions
We present a discounted stochastic game with a continuum of states, finitely many players and actions, such that although all transitions are absolutely continuous w.r.t. a fixed measure, it possesses no stationary equilibria. This absolute continuity condition has been assumed in many equilibrium existence results, and the game presented here complements a recent example of ours of a game with no stationary equilibria but which possess deterministic transitions. We also show that if one allows for compact action spaces, even games with state-independent transitions need not possess stationary equilibria.
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