A Stochastic Game without Approximate Equilibria

Abstract

A game has approximate equilibria if for every $\epsilon >0$ there is an $\epsilon$-equilibrium. We show that there is a stochastic game that lacks approximate equilibria. This game has finitely many players and actions, their payoffs are Borel measurable functions on the pathways of play, and all players have perfect knowledge of the past histories and the present state.

The proof is flawed