Learning Equilibria in Coordination Games via Minorization-Maximization

TL;DR

This paper introduces a regularized approach to find unique equilibria in coordination games with irrational agents, using a minorization-maximization algorithm that outperforms traditional methods.

Contribution

It proposes a novel regularization and a minorization-maximization based iterative scheme to efficiently learn potential-optimal equilibria in complex coordination games.

Findings

The method converges to the potential-optimal equilibrium.

It exhibits superior convergence compared to gradient and best response methods.

The equilibrium is an $psilon$-approximation of the original game.

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 $\epsilon-$equilibrium of the original game, where $\epsilon$ 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.