Network games under strategic complementarities

Mohamed Belhaj,Yann Bramoullé,Frédéric Deroïan

doi:10.1016/j.geb.2014.10.009

Abstract

We study network games under strategic complementarities. Agents are embedded in a fixed network. They choose a positive, continuous action and interact with their network neighbors. Interactions are positive and actions are bounded from above. We first derive new sufficient conditions for uniqueness, covering all concave as well as some non-concave best responses. We then study the relationship between position and action and identify situations where a more central agent always plays a higher action in equilibrium. We finally analyze comparative statics. We show that a shock may not propagate throughout the entire network and uncover a general pattern of decreasing interdependence.

Highlights

In this paper, we study network games under strategic complementarities
When the graph is symmetric and structured around a geometric center, like the line, action is aligned with centrality in extremal equilibria
Ballester et al (2006) study network games under linear best responses and small network effects. They find that the equilibrium is unique and that action is aligned with Bonacich centrality

Summary

Introduction

We study network games under strategic complementarities. Agents are embedded in a fixed network and choose a positive, continuous action. When the graph is symmetric and structured around a geometric center, like the line, action is aligned with centrality in extremal equilibria These results hold for any curvature of the best response below the upper bound. A large part of this literature to date has studied games with linear best responses.3 Ballester et al (2006) study network games under linear best responses and small network effects They find that the equilibrium is unique and that action is aligned with Bonacich centrality. Hiller (2012) and Baetz (forthcoming) analyze network games with homogeneous concave best responses They establish uniqueness by applying Kennan (2001)’s results.

The model

Uniqueness

Network position and action

Comparative statics and broken interdependence

Conclusion