Stochastic Graphon Games: I. The Static Case

TL;DR

This paper studies static network games with many players, establishing existence, uniqueness, and convergence of strategies, and demonstrating how graphon game equilibria approximate finite-player Nash equilibria, with applications and explicit examples.

Contribution

It introduces the concept of graphon games for static networks, proving key theoretical results and connecting them to finite-player games and mean field models.

Findings

Existence and uniqueness of equilibria in graphon games.

Finite-player strategies converge to graphon game solutions.

Graphon equilibria approximate finite-player Nash equilibria.

Abstract

We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs for the graphon games. We also show that equilibrium strategy profiles of a graphon game provide approximate Nash equilibria for the finite-player games. Connections with mean field games and central planner optimization problems are discussed. Motivating applications are presented and explicit computations of their Nash equilibria and social optimal strategies are provided.