Natural Strategic Ability in Stochastic Multi-Agent Systems
This work addresses the complexity of verifying strategic behaviors in stochastic multi-agent systems, which is an incremental extension of deterministic frameworks.
The paper tackles the problem of modeling strategic ability in stochastic multi-agent systems by extending natural strategies to probabilistic settings, showing that model-checking for NatPATL is NP-complete with deterministic strategies and EXPSPACE without restrictions.
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 model-checking 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 NP-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*.