Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs

TL;DR

This paper proves that all two-player stochastic games with finite states, actions, and shift-invariant payoffs have approximate equilibria, extending the understanding of equilibrium existence in complex dynamic settings.

Contribution

It establishes the existence of $ ext{ε}$-equilibria in a broad class of stochastic games with shift-invariant payoffs, a significant generalization.

Findings

Existence of $ ext{ε}$-equilibria for all $ ext{ε}>0$

Applicable to games with finite states and actions

Payoffs are bounded, Borel-measurable, and shift-invariant

Abstract

We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.