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arXiv · 2301.10697

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

Benjamin Bordais·Patricia Bouyer·Stéphane Le Roux
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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.

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Benjamin Bordais, Patricia Bouyer, Stéphane Le Roux. 2023-01-25. Sub-game optimal strategies in concurrent games with prefix-independent objectives. https://arxiv.org/abs/2301.10697

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