Graphon games: A statistical framework for network games and interventions

TL;DR

This paper introduces graphon games as a new framework for analyzing large network games, enabling efficient equilibrium approximation and intervention design based on a continuum model.

Contribution

The paper develops the concept of graphon games, linking finite network equilibria to a continuum limit, and demonstrates how to design asymptotically optimal interventions efficiently.

Findings

Graphon equilibria approximate large network game equilibria.

Interventions based on graphon models are computationally efficient.

The framework applies to real-world data, such as rural villages.

Abstract

In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. We first introduce a new class of infinite population games, termed graphon games, where a continuum of heterogeneous agents interact according to a graphon. After studying properties of equilibria in graphon games, we show that graphon equilibria can approximate equilibria of large network games sampled from the graphon. We next show that, under some regularity assumptions, the graphon approach enables the design of asymptotically optimal interventions via the solution of an optimization problem with much lower dimension than the one based on the entire network structure. We illustrate our framework on a synthetic dataset of rural villages and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.