Social Interactions in Large Networks: A Game Theoretic Approach

TL;DR

This paper develops a game theoretic model for social interactions in large networks, establishing equilibrium properties, a novel network decaying dependence condition, and an efficient estimation method, demonstrated through application and simulations.

Contribution

It introduces a new network decaying dependence condition and provides a feasible estimation approach for large network games with asymmetric information.

Findings

Existence and uniqueness of equilibrium established.

Network decaying dependence condition proven.

Efficient estimation method demonstrated with real data and simulations.

Abstract

This paper studies social interactions in a game theoretic model with players in a large social network. We consider observations from one single equilibrium of a large network game with asymmetric information, in which each player chooses an action from a finite set and is subject to interactions with her friends. Simple assumptions about the structure are made to establish the existence and uniqueness of equilibrium. In particular, we show that the equilibrium strategies satisfy a network decaying dependence (NDD) condition requiring that dependence between any two players' decisions decays with their network distance. The formulation of such an NDD property is novel and serves as the basis for statistical inference. Further, we establish the identification of the structural model and introduce a computationally feasible and efficient estimation method. We illustrate the estimation method with an actual application to college attendance, as well as in Monte Carlo experiments.