Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly

TL;DR

This paper introduces a variational inequality framework for solving stochastic Nash equilibrium problems, especially in oligopoly markets with data described by probability distributions, advancing the analysis of uncertain strategic interactions.

Contribution

It develops a novel approach using monotone variational inequalities in probabilistic spaces for stochastic Nash problems, with an application to Cournot oligopoly models.

Findings

Provides a new mathematical formulation for stochastic Nash equilibria.

Demonstrates the applicability to oligopoly market models with probabilistic data.

Lays groundwork for future computational methods in stochastic game theory.

Abstract

In this note we investigate stochastic Nash equilibrium problems by means of monotone variational inequalities in probabilistic Lebesgue spaces. We apply our approach to a class of oligopolistic market equilibrium problems where the data are known through their probability distributions.