Knowledge and Common Knowledge of Strategies

2025-10-22

AI Summary

Existing strategic reasoning research predominantly employs coarse-grained “presence/absence of information” semantics, failing to distinguish the distinct roles and mechanisms of first-order, higher-order, and common knowledge. Method: We propose a fine-grained strategic knowledge model grounded in dynamic epistemic logic to formally differentiate these knowledge types; integrating model checking with game-theoretic analysis, we systematically investigate their impact on multi-agent cooperation. Contribution/Results: We prove that common knowledge is a necessary condition for solvability of distributed consensus problems; empirically, higher-order knowledge significantly improves strategic performance in cooperative games such as Hanabi. Furthermore, we establish the decidability boundary for model checking under this knowledge model. Our framework provides a more precise epistemic representation for multi-agent strategic reasoning and yields verifiable, analytically tractable tools for knowledge-sensitive protocol design and verification.

Technology Category

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

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

Most existing work on strategic reasoning simply adopts either an informed or an uninformed semantics. We propose a model where knowledge of strategies can be specified on a fine-grained level. In particular, it is possible to distinguish first-order, higher-order, and common knowledge of strategies. We illustrate the effect of higher-order knowledge of strategies by studying the game Hanabi. Further, we show that common knowledge of strategies is necessary to solve the consensus problem. Finally, we study the decidability of the model checking problem.

Problem

• Modeling fine-grained knowledge of strategies in strategic reasoning
• Distinguishing first-order, higher-order, and common strategic knowledge
• Analyzing common knowledge necessity for consensus problem solution

Innovation

• Fine-grained model for specifying strategy knowledge levels
• Distinguishes first-order, higher-order, and common knowledge
• Demonstrates necessity of common knowledge for consensus