A Game-Theoretic Framework for Network Formation in Large Populations

TL;DR

This paper introduces a game-theoretic model for network formation in large populations, analyzing equilibrium conditions, uniqueness, and effects of various settings through theoretical and numerical methods.

Contribution

It develops a novel network formation model where agents' interactions depend on both their own and others' indices, extending graphon game theory.

Findings

Established existence and uniqueness of Nash equilibria.

Derived optimality conditions via forward-backward stochastic differential equations.

Numerical experiments illustrate the impact of different model parameters.

Abstract

In this paper, we study a model of network formation in large populations. Each agent can choose the strength of interaction (i.e. connection) with other agents to find a Nash equilibrium. Different from the recently-developed theory of graphon games, here each agent's control depends not only on her own index but also on the index of other agents. After defining the general model of the game, we focus on a special case with piecewise constant graphs and we provide optimality conditions through a system of forward-backward stochastic differential equations. Furthermore, we show the uniqueness and existence results. Finally, we provide numerical experiments to discuss the effects of different model settings.