Absorbing Blackwell Games

TL;DR

This paper presents a simplified proof for the existence of approximate equilibria in two-player absorbing stochastic games with tail-measurable payoffs, building on recent mathematical tools and classical methods.

Contribution

It offers a more straightforward proof for $ extepsilon$-equilibria in two-player absorbing games with tail-measurable payoffs, enhancing understanding and accessibility.

Findings

Simplified proof for $ extepsilon$-equilibrium existence

Applicable to two-player absorbing games with tail-measurable payoffs

Combines recent mathematical tools with classical methods

Abstract

It was shown in Flesch and Solan (2022) with a rather involved proof that all two-player stochastic games with finite state and action spaces and shift-invariant payoffs admit an $\epsilon$-equilibrium, for every $\epsilon>0$. Their proof also holds for two-player absorbing games with tail-measurable payoffs. In this paper we provide a simpler proof for the existence of $\epsilon$-equilibrium in two-player absorbing games with tail-measurable payoffs, by combining recent mathematical tools for such payoff functions with classical tools for absorbing games.