Learning Equilibria in Coordination Games via Minorization-Maximization

2026-05-13

AI Summary

This study addresses the equilibrium selection problem in coordination games where agents exhibit irrational perceptions of costs or rewards, leading to multiple equilibria. By introducing regularization to construct a strictly concave potential function, the work uniquely identifies a potential-optimal equilibrium. It innovatively applies the Minorization-Maximization (MM) algorithm—used here for the first time in equilibrium learning for coordination games—to develop an iterative method that selects an ε-equilibrium of the original game based on the regularized potential function. Theoretical analysis and empirical experiments demonstrate that the proposed algorithm converges reliably to the potential-optimal equilibrium and significantly outperforms gradient-based and best-response dynamics in terms of both convergence speed and stability.

Abstract

This paper considers games where the utilities for agents are the sum of a term proportional to a social utility, and another term that is an individual cost or reward. The agents are assumed to be irrational in their perception of the individual cost or reward. The multi equilibrium game is regularized, and its strictly concave potential function is used to select a unique equilibrium. This selected equilibrium is shown to be an $ε-$equilibrium of the original game, where $ε$ is parametrized by the regularizing function. A minorization-maximization based iterative learning scheme is proposed to learn equilibria in this game. This scheme converges to the potential-optimal equilibrium, and has superior convergence behaviour in comparison to gradient and best response methods.

Problem

• Coordination Games
• Equilibrium Selection
• Irrational Agents
• Potential Function
• ε-Equilibrium

Innovation

• Minorization-Maximization
• coordination games
• potential function
• ε-equilibrium
• iterative learning