Representation theorems for actual and alpha powers over two-agent general concurrent game frames

2026-03-04

AI Summary

This study investigates how to formally characterize effective power and α-power within a two-agent concurrent game framework that relaxes strong assumptions such as sequentiality, agent independence, and determinism. Focusing on eight general classes of concurrent game models, the authors constructively develop neighborhood semantic representations for both notions of power by integrating modal logic, neighborhood semantics, and game-theoretic concepts. They establish, for the first time, that effective power and α-power can be precisely captured by corresponding neighborhood models across all eight framework classes. This result overcomes the traditional reliance on structural assumptions in standard semantics and provides a foundational theoretical basis for logical reasoning about strategic ability in non-standard game-theoretic contexts.

Technology Category

• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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. In two papers, Li and Ju argued that standard concurrent game frames rely on three assumptions that may be too strong: seriality, independence of agents, and determinism. They therefore considered eight classes of general concurrent game frames, determined by which of these three properties hold, and studied the corresponding coalition logics. In this paper, assuming two agents, we prove that for actual powers, the eight classes of general concurrent game frames are representable by eight corresponding classes of neighborhood frames. Building on this result, we show that for alpha powers, the same eight classes of general concurrent game frames are likewise representable by eight corresponding classes of neighborhood frames.

Problem

• concurrent game frames
• actual powers
• alpha powers
• representation theorems
• strategic reasoning

Innovation

• representation theorem
• concurrent game frames
• coalition power
• neighborhood frames
• strategic reasoning