Graphon Games: A Statistical Framework for Network Games and Interventions

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. To this end, we introduce a new class of infinite population games, termed graphon games, in which a continuum of heterogeneous agents interact according to a graphon, and we show that equilibria of graphon games can be used to approximate equilibria of large network games sampled from the graphon. This suggests a new approach for design of interventions and parameter inference based on the limiting infinite population graphon game. We show that, under some regularity assumptions, such 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 data set and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.