Endogenous clustering and analogy-based expectation equilibrium

2025-05-19

AI Summary

This paper investigates how players endogenously partition opponents’ behaviors in two-player games to minimize prediction error, introducing the novel solution concept of “Clustered Analogy-Based Expectational Equilibrium” (CABEE). Methodologically, it establishes the first clustering equilibrium framework wherein analogy-based partitioning and strategy choice are jointly endogenous, formally modeling analogy reasoning and rigorously proving the existence of CABEE. Theoretically, it distinguishes between self-repelling and self-attracting environments, revealing new mechanisms through which the former induces belief heterogeneity and the latter generates equilibrium multiplicity—thereby extending the theoretical frontiers of belief formation and equilibrium selection. Applicationally, it identifies novel forms of equilibrium multiplicity and belief divergence across multiple economic settings, providing a structured analytical tool for understanding strategic interaction under bounded rationality.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Normal-form two-player games are categorized by players into K analogy classes so as to minimize the prediction error about the behavior of the opponent. This results in Clustered Analogy-Based Expectation Equilibria in which strategies are analogy-based expectation equilibria given the analogy partitions and analogy partitions minimize the prediction errors given the strategies. We distinguish between environments with self-repelling analogy partitions in which some mixing over partitions is required and environments with self-attractive partitions in which several analogy partitions can arise, thereby suggesting new channels of belief heterogeneity and equilibrium multiplicity. Various economic applications are discussed.

Problem

• Categorize games into analogy classes to minimize prediction errors
• Study equilibrium with self-repelling vs self-attractive analogy partitions
• Explore belief heterogeneity and equilibrium multiplicity in economic contexts

Innovation

• Categorize games into K analogy classes
• Minimize prediction error via analogy partitions
• Distinguish self-repelling vs self-attractive partitions