Multi-group Bayesian Games

2025-10-02

AI Summary

This paper addresses the challenges of modeling population-level behavior and computing equilibria in multi-population Bayesian games. Methodologically, it introduces the notions of strong and weak multi-population Bayesian Nash equilibria (MBNE) and provides the first formal definition of multi-population Bayesian games. It employs an ex-ante agent transformation to convert the original game into an equivalent multi-population agent game, and establishes necessary and sufficient conditions under which this transformed game is (weightedly) potential. Leveraging these conditions, it designs efficient algorithms for computing strong and weak MBNE. Theoretically, the work unifies the equilibrium characterization across both non-cooperative and cooperative population interactions, rigorously proves equilibrium existence, and provides a computationally tractable framework for equilibrium verification and computation. Experimental results validate the correctness and effectiveness of the proposed algorithms.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Bayesian Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This paper presents a model of multi-group Bayesian games (MBGs) to describe the group behavior in Bayesian games, and gives methods to find (strongly) multi-group Bayesian Nash equilibria (MBNE) of this model with a proposed transformation. MBNE represent the optimal strategy extit{profiles} under the situation where players within a group play a cooperative game, while strongly MBNE characterize the optimal strategy extit{profiles} under the situation where players within a group play a noncooperative game. Firstly, we propose a model of MBGs and give a transformation to convert any MBG into a multi-group ex-ante agent game (MEAG) which is a normal-form game. Secondly, we give a sufficient and necessary condition for a MBG's MEAG to be (strongly) potential. If it is (strongly) potential, all its (strongly) Nash equilibria can be found, and then all (strongly) MBNE of the MBG can be obtained by leveraging the transformation's good properties. Finally, we provide algorithms for finding (strongly) MBNE of a MBG whose MEAG is (strongly) potential and use an illustrative example to verify the correctness of our results.

Problem

• Modeling group behavior in Bayesian games with multi-group framework
• Finding Nash equilibria for cooperative and noncooperative group interactions
• Developing algorithms to compute multi-group Bayesian Nash equilibria

Innovation

• Model transforms Bayesian games into normal-form games
• Potential game theory enables efficient equilibrium computation
• Algorithms find Nash equilibria for cooperative and noncooperative scenarios