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

arXiv: https://arxiv.org/abs/2507.17183 · HTML: https://mlsanity.com/paper/2507.17183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Graphical Models for Game Theory](https://mlsanity.com/paper/1301.2281/) (2013)
- [Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality](https://mlsanity.com/paper/2106.12928/) (2021)
- [Online Multi-Agent Forecasting with Interpretable Collaborative Graph Neural Network](https://mlsanity.com/paper/2107.00894/) (2021)
- [Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory](https://mlsanity.com/paper/2012.03083/) (2020)
- [The route to chaos in routing games: When is Price of Anarchy too optimistic?](https://mlsanity.com/paper/1906.02486/) (2019)
- [Fast and Furious Learning in Zero-Sum Games: Vanishing Regret with Non-Vanishing Step Sizes](https://mlsanity.com/paper/1905.04532/) (2019)
- [Dynamics-Adaptive Continual Reinforcement Learning via Progressive Contextualization](https://mlsanity.com/paper/2209.00347/) (2022)
- [Follow-the-Regularized-Leader Routes to Chaos in Routing Games](https://mlsanity.com/paper/2102.07974/) (2021)
- [Dynamic Slimmable Denoising Network](https://mlsanity.com/paper/2110.08940/) (2021)
- [3D-TOGO: Towards Text-Guided Cross-Category 3D Object Generation](https://mlsanity.com/paper/2212.01103/) (2022)
- [The Dynamics of Q-learning in Population Games: a Physics-Inspired Continuity Equation Model](https://mlsanity.com/paper/2203.01500/) (2022)
- [Heterogeneous Beliefs and Multi-Population Learning in Network Games](https://mlsanity.com/paper/2301.04929/) (2023)

## Built on by (most cited first, 1 of 1)

- [Ultracoarse Equilibria and Ordinal-Folding Dynamics in Operator-Algebraic Models of Infinite Multi-Agent Games](https://mlsanity.com/paper/2507.19694/) (2025)

## Abstract (arXiv)

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.