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arXiv · 2409.18155

Non-cooperative rational synthesis problem for probabilistic strategies

So Koide·Yoshiaki Takata·Hiroyuki Seki
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Abstract

We study the decidability and complexity of non-cooperative rational synthesis problem (abbreviated as NCRSP) for some classes of probabilistic strategies. We show that NCRSP for stationary strategies and Muller objectives is in 3-EXPTIME, and if we restrict the strategies of environment players to be positional, NCRSP becomes NEXPSPACE solvable. On the other hand, NCRSP_>, which is a variant of NCRSP, is shown to be undecidable even for pure finite-state strategies and terminal reachability objectives. Finally, we show that NCRSP becomes EXPTIME solvable if we restrict the memory of a strategy to be the most recently visited t vertices where t is linear in the size of the game.

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So Koide, Yoshiaki Takata, Hiroyuki Seki. 2024-09-26. Non-cooperative rational synthesis problem for probabilistic strategies. https://arxiv.org/abs/2409.18155

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