State and path coalition effectivity models of concurrent multi-player games

Abstract

We consider models of multi-player games where abilities of players and coalitions are defined in terms of sets of outcomes which they can effectively enforce. We extend the well-studied state effectivity models of one-step games in two different ways. On the one hand, we develop multiple state effectivity functions associated with different long-term temporal operators. On the other hand, we define and study coalitional path effectivity models where the outcomes of strategic plays are infinite paths. For both extensions we obtain representation results with respect to concrete models arising from concurrent game structures. We also apply state and path coalitional effectivity models to provide alternative, arguably more natural and elegant semantics to the alternating-time temporal logic ATL*, and discuss their technical and conceptual advantages.

Strategic Abilities of Asynchronous Agents: Semantic Side Effects and How to Tame Them

“…In this sense, the possible behaviors of an agent system should be understood via the set of possible execution trees, rather than a single tree. This is consistent with the theoretical model of MAS in (Goranko and Jamroga 2015), based on path effectivity functions.…”