Blackwell-Optimal Strategies in Priority Mean-Payoff Games

TL;DR

This paper establishes a connection between discounted and priority mean-payoff games by showing that strategies optimal for near-1 discount factors are also optimal for priority mean-payoff games, unifying these game classes.

Contribution

It demonstrates that deterministic memoryless strategies optimal in discounted games with high discount factors are also optimal in priority mean-payoff games, revealing a strong theoretical link.

Findings

Optimal strategies for discounted games extend to priority mean-payoff games.

A strong link between discounted and priority mean-payoff games is established.

The results unify two important classes of stochastic games.

Abstract

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes.