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Strategic planning for probabilistic games with incomplete information

Alternating-time Temporal Logic (ATL) [1] is used to reason about strategic abilities of agents. Aiming at strategies that can realistically be implemented in software, many variants of ATL study a setting where strategies may only take available information into account [7]. Another generalization of ATL is Probabilistic ATL [4], where strategies achieve their goal with a certain probability. 
 
We introduce a semantics of ATL that takes into account both of these aspects. We prove that our semantics allows simulation relations similar in spirit to usual bisimulations, and has a decidable model checking problem in the case of memoryless strategies (for memory-dependent strategies the problem is undecidable).