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.
Highlights
A wide variety of multi-player games can be modeled by so called ‘multi-player game models’ [16,29], a.k.a. ‘concurrent game models’ [6]
Strategies in multi-step games A path in a concurrent game structure (CGS)/concurrent game model (CGM) is an infinite sequence of states that can result from subsequent transitions in the structure
Since P-Additivity is strictly stronger than P-Superadditivity, by Theorems 4 and 5 we get the following: Corollary 5 There are concurrent game structures generating path effectivity functions that cannot be obtained in stit frames
Summary
A wide variety of multi-player games can be modeled by so called ‘multi-player game models’ [16,29], a.k.a. ‘concurrent game models’ [6]. In this paper we study how multi-step games can be modeled and characterized in terms of effectivity of coalitions with respect to possible outcome states on one hand, and outcome behaviours on the other. (ii) To develop the analogous notion of coalitional path effectivity representing the powers of coalitions in multi-step games to ensure long-term behaviors, and to provide semantics for ATL* based on it;. 4 we develop and study effectivity models based on paths We show how they provide semantics to ATL*, and identify appropriate “playability” conditions, which we use to establish correspondences between powers of coalitions in the abstract models and strategic abilities of coalitions in concurrent game models. We show an application of our characterization results to the well-known stit models of agency
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