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We introduce QAPI (quantified ATL with probabilism and incomplete information), which extends epistemic and probabilistic ATL with a flexible mechanism to reason about strategies in the object language, allowing very flexible treatment of the behavior of the “counter-coalition”. QAPI can express complex strategic properties such as equilibria. We show how related logics can be expressed in QAPI, provide bisimulation relations, and study the issues arising from the interplay between quantifiers and both epistemic and temporal operators.

Quantified Epistemic and Probabilistic ATL