Representation theorems for actual and alpha powers over general concurrent game frames without assuming independence of agents

2026-07-12

AI Summary

This study investigates the representation of effective and α-power for coalitions within generalized concurrent game frameworks that abandon the assumption of agent independence. By deconstructing structural assumptions of standard concurrent games—such as sequentiality, determinism, and agent independence—the authors construct eight generalized frameworks and focus on four classes where agent independence does not hold. Integrating modal logic semantics, neighborhood semantics, and game-theoretic reasoning, they employ structural decomposition and bisimulation techniques to establish, for the first time, complete representation theorems mapping these two notions of power onto corresponding neighborhood frames. This work extends the semantic foundations of strategic reasoning logics and provides novel formal tools for reasoning about environments with interdependent agents.

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.

Problem

• concurrent game frames
• actual powers
• alpha powers
• representation theorems
• independence of agents

Innovation

• concurrent game frames
• actual powers
• alpha powers
• neighborhood frames
• representation theorems