Representation theorems for actual and alpha powers over general concurrent game frames without assuming independence of agents
2026-07-12 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study different ways to understand the power of groups (coalitions) in games where players make moves at the same time. They focus on two types of power: alpha powers, where a group can ensure outcomes fall within a certain set, and actual powers, which add an extra condition about how the group's actions relate to those outcomes. They explore more general models that relax some standard game assumptions and show how these models connect to mathematical structures called neighborhood frames. Their results show a precise correspondence between these game models and neighborhood frames for both types of coalition power when agents are not assumed to be independent.
concurrent game framescoalition poweralpha powersactual powersserialityindependence of agentsdeterminismneighborhood framesstrategic reasoning
Authors
Zixuan Chen, Fengkui Ju, Thomas Agotnes
Abstract
Concurrent game frames are a standard semantic framework for logics of strategic reasoning. Two notions of coalition power can be derived from such frames: alpha powers and actual powers. An alpha power of a coalition is a set of possible futures such that the coalition has an action that forces the resulting future to lie in that set. An actual power of a coalition is a set of possible futures satisfying the following condition: the coalition has an action such that (1) the action forces the resulting future to lie in the set, and (2) every future in the set is compatible with that action. Recent generalizations of concurrent game frames separate three structural assumptions built into the standard model: seriality, independence of agents, and determinism. This yields eight classes of general concurrent game frames. In this paper, we prove that for actual powers, the four classes of general concurrent game frames, where independence of agents is not assumed, are representable by four corresponding classes of neighborhood frames. Building on this result, we show that for alpha powers, the same four classes of general concurrent game frames are likewise representable by four corresponding classes of neighborhood frames.