Computation of Cournot-Nash equilibria by entropic regularization

TL;DR

This paper introduces a numerical method using entropic regularization to compute Cournot-Nash equilibria in continuum games, extending the approach to multi-population models.

Contribution

It applies entropic regularization to optimal transport-based equilibrium computation, enabling efficient numerical solutions for complex game models with multiple populations.

Findings

Effective numerical approximation of equilibria

Extension to multi-population models

Demonstrated convergence and computational efficiency

Abstract

We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7]. We then use the powerful entropic regularization technique to approximate the problem and solve it numerically in various cases. We also consider the extension to some models with several populations of players.