From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem

TL;DR

This paper explores the connection between Nash and Cournot-Nash equilibria using optimal transport theory, especially as the number of players grows large, providing new insights into equilibrium analysis.

Contribution

It introduces a novel approach linking Nash and Cournot-Nash equilibria through the Monge-Kantorovich problem, enhancing understanding of large-player game dynamics.

Findings

Establishes a theoretical link between Nash and Cournot-Nash equilibria.

Uses optimal transport to analyze equilibria as players increase.

Provides a framework for studying large-scale strategic interactions.

Abstract

The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article we emphasize the role of optimal transport theory in: 1) the passage from Nash to Cournot-Nash equilibria as the number of players tends to infinity, 2) the analysis of Cournot-Nash equilibria.