Graphon games

The study of strategic behavior in large scale networks via standard game theoretical methods is a challenging, if not intractable, task. In this paper, we propose a way to approximate games played over networks of increasing size, by using the graph limiting concept of graphon. To this end, we introduce the new class of graphon games for populations of infinite size. We investigate existence and uniqueness properties of the Nash equilibrium of graphon games and we derive upper bounds for the distance between the Nash equilibria of the infinite population graphon game and of finite population sampled network games. Finally, we derive a closed form expression for the Nash equilibrium of linear quadratic graphon games and we illustrate its relation to Bonacich centrality.