Constant Payoff Property in Zero-Sum Stochastic Games with a Finite Horizon

TL;DR

This paper proves that in long finite zero-sum stochastic games, players can adopt strategies ensuring the average payoff remains close to the game's value throughout, extending the constant payoff property beyond previously known game types.

Contribution

It establishes the constant payoff property for finite zero-sum stochastic games with sufficiently long durations, generalizing prior results.

Findings

Existence of approximately optimal strategies with constant payoff property

The property holds for sufficiently long game durations

Extends the constant payoff property beyond absorbing and discounted games

Abstract

This paper examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game remains close to the value. This property, known as the \textit{constant payoff property}, was previously established only for absorbing games and discounted stochastic games.