Unattainability of Common Knowledge in Asymmetric Games with Imperfect Information

2025-01-08

AI Summary

This paper investigates the attainability of common knowledge in extremely asymmetric incomplete-information games: one agent can act but has no knowledge of the state, while the other knows the state perfectly yet cannot act or observe. Under this strict separation of informational and behavioral capabilities, we construct a multi-agent epistemic model grounded in Kripke structures and modal logic, and formally prove that common knowledge of the current state is unattainable. This result provides the first formal refutation of common knowledge realizability in such games, exposing a fundamental boundary on strategic knowledge formation. The findings establish a new theoretical limit for knowledge coordination in distributed decision-making, human–machine collaboration, and mechanism design—highlighting inherent constraints when epistemic and agential capacities are fully decoupled.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Knowledge Representation and Reasoning: Common-Sense Reasoning
• Multiagent Systems: Mechanism Design

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed.

Problem

• Asymmetric Games
• Information Sharing
• Strategy Limitation

Innovation

• Asymmetric Information
• Common Knowledge
• Game Model