Natural Strategic Ability in Stochastic Multi-Agent Systems

Strategies synthesized using formal methods can be complex and often require infinite memory, which does not correspond to the expected behavior when trying to model Multi-Agent Systems (MAS). To capture such behaviors, natural strategies are a recently proposed framework striking a balance between the ability of agents to strategize with memory and the modelchecking complexity, but until now has been restricted to fully deterministic settings. For the first time, we consider the probabilistic temporal logics PATL and PATL * under natural strategies (NatPATL and NatPATL * , resp.). As main result we show that, in stochastic MAS, NatPATL model-checking is ∆ P 2 -complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL * with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATL * . * This is an extended version of the same title paper that appeared at AAAI 2024, containing a technical appendix with proof details. In this version, we also correct the proof of Theorem 3. We would like to thank Wojtek Jamroga for spotting the problem and alerting us.