A Proof of the Vieille Result Using a Kind of Discount Factor

TL;DR

This paper presents an alternative proof for the existence of approximate equilibria in certain stochastic games, utilizing a state-specific discount factor approach that aligns with traditional methods in simpler cases.

Contribution

It introduces a novel proof technique employing a state-specific discount factor, providing a different perspective on Vieille's result for stochastic games.

Findings

Existence of approximate equilibria in the specified stochastic games

The proof method is similar to conventional discounting when only one non-absorbing state exists

Provides an alternative approach to Vieille's original proof

Abstract

We give an alternative proof that every two-person non-zero-sum absorbing positive recursive stochastic game with finitely many states has approximate equilibria, a result proven by Nicolas Vieille. Our proof uses a state specific discount factor which is similar to the conventional discount factor only when there is only one non-absorbing state.