Existence of Bayesian Equilibria in Incomplete Information Games without Common Priors

2025-04-22

AI Summary

This paper addresses the existence of Bayesian equilibria in incomplete-information games without a common prior, specifically under mutually inconsistent beliefs among players. To overcome the restrictive nature of the standard common-prior assumption, we extend the measure-theoretic notion of absolute continuity—from information structures to belief systems—introducing a novel analytical framework based on *generalized belief absolute continuity*. This framework accommodates rich type spaces and infinite belief hierarchies, and rigorously establishes the existence of Bayesian equilibria without invoking a common prior. Our result generalizes the Milgrom–Weber theory of information structures and provides a foundational existence guarantee for Bayesian equilibria in games with complex, heterogeneous belief structures—such as those arising in financial markets and mechanism design.

Technology Category

Game Theory and Economic Paradigms: Mechanism DesignMultiagent Systems: Mechanism DesignReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

We consider incomplete information finite-player games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolutely continuous information in Milgrom and Weber (1985), and prove that a Bayesian equilibrium exists under broad conditions. Applying these results to games with rich type spaces that accommodate infinite belief hierarchies, we show that when the analyst's game has a type space satisfying absolute continuity of beliefs, the actual game played according to the belief hierarchies induced by the type space has a Bayesian equilibrium for a wide class of games. We provide examples that illustrate practical applications of our findings.

Problem

• Existence of Bayesian equilibria in inconsistent belief games
• Extending absolute continuity to non-common prior settings
• Equilibrium analysis for infinite belief hierarchy games

Innovation

• Extends absolute continuity of beliefs concept
• Proves Bayesian equilibrium under broad conditions
• Applies to games with infinite belief hierarchies