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.
@article{arxiv.2409.18155,
title = {Non-cooperative rational synthesis problem for probabilistic strategies},
author = {So Koide and Yoshiaki Takata and Hiroyuki Seki},
journal= {arXiv preprint arXiv:2409.18155},
year = {2024}
}