Sub-game optimal strategies in concurrent games with prefix-independent objectives

TL;DR

This paper characterizes subgame optimal strategies in concurrent stochastic games with prefix-independent objectives and explores conditions under which these strategies can be simplified to positional strategies, with applications to classical objectives.

Contribution

It provides a novel characterization of subgame optimal strategies and establishes memory transfer results, simplifying strategy complexity in various classes of concurrent games.

Findings

Conditions under which subgame optimal strategies are positional

Memory transfer results for prefix-independent objectives

Applications to classical objectives like B"uchi and parity

Abstract

We investigate concurrent two-player win/lose stochastic games on finite graphs with prefix-independent objectives. We characterize subgame optimal strategies and use this characterization to show various memory transfer results: 1) For a given (prefix-independent) objective, if every game that has a subgame almost-surely winning strategy also has a positional one, then every game that has a subgame optimal strategy also has a positional one; 2) Assume that the (prefix-independent) objective has a neutral color. If every turn-based game that has a subgame almost-surely winning strategy also has a positional one, then every game that has a finite-choice (notion to be defined) subgame optimal strategy also has a positional one. We collect or design examples to show that our results are tight in several ways. We also apply our results to B\"uchi, co-B\"uchi, parity, mean-payoff objectives, thus yielding simpler statements.