Regret Minimization in Population Network Games: Vanishing Heterogeneity and Convergence to Equilibria

Fuente: arXiv
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Main Authors: Hu, Die, Hu, Shuyue, Mu, Chunjiang, Fan, Shiqi, Chu, Chen, Liu, Jinzhuo, Wang, Zhen
Format: Preprint
Published: 2025
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author Hu, Die
Hu, Shuyue
Mu, Chunjiang
Fan, Shiqi
Chu, Chen
Liu, Jinzhuo
Wang, Zhen
author_facet Hu, Die
Hu, Shuyue
Mu, Chunjiang
Fan, Shiqi
Chu, Chen
Liu, Jinzhuo
Wang, Zhen
contents Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth regret-matching drives a large number of heterogeneous agents with diverse initial policies toward unified behavior. By modeling the system state as a probability distribution of regrets and analyzing its evolution through the continuity equation, we uncover a key phenomenon in diverse multi-agent settings: the variance of the regret distribution diminishes over time, leading to the disappearance of heterogeneity and the emergence of consensus among agents. This universal result enables us to prove convergence to quantal response equilibria in both competitive and cooperative multi-agent settings. Our work advances the theoretical understanding of multi-agent learning and offers a novel perspective on equilibrium selection in diverse game-theoretic scenarios.
format Preprint
id arxiv_https___arxiv_org_abs_2507_17183
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Regret Minimization in Population Network Games: Vanishing Heterogeneity and Convergence to Equilibria
Hu, Die
Hu, Shuyue
Mu, Chunjiang
Fan, Shiqi
Chu, Chen
Liu, Jinzhuo
Wang, Zhen
Computer Science and Game Theory
Artificial Intelligence
Multiagent Systems
Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth regret-matching drives a large number of heterogeneous agents with diverse initial policies toward unified behavior. By modeling the system state as a probability distribution of regrets and analyzing its evolution through the continuity equation, we uncover a key phenomenon in diverse multi-agent settings: the variance of the regret distribution diminishes over time, leading to the disappearance of heterogeneity and the emergence of consensus among agents. This universal result enables us to prove convergence to quantal response equilibria in both competitive and cooperative multi-agent settings. Our work advances the theoretical understanding of multi-agent learning and offers a novel perspective on equilibrium selection in diverse game-theoretic scenarios.
title Regret Minimization in Population Network Games: Vanishing Heterogeneity and Convergence to Equilibria
topic Computer Science and Game Theory
Artificial Intelligence
Multiagent Systems
url https://arxiv.org/abs/2507.17183