A Model for Social Network Formation: Efficiency, Stability and Dynamics

TL;DR

This paper presents a simple model for social network formation balancing connection costs and reach benefits, analyzing the stability, efficiency, and dynamics of resulting networks with convergence guarantees.

Contribution

It introduces a new network formation model with proven convergence to stable networks and characterizes efficient network structures under various parameters.

Findings

Asynchronous edge dynamics always converge to stable networks.

Convergence is fast for certain parameter ranges.

The set of fixed points forms a nontrivial class of networks.

Abstract

We introduce a simple network formation model for social networks. Agents are nodes, connecting to another agent by building a directed edge (or accepting a connection from another agent) has a cost, and reaching (or being reached by) other agents via short directed paths has a benefit; in effect, an agent wants to reach others quickly, but without the cost of directly connecting each and every one. We prove that asynchronous edge dynamics always converge to a stable network; in fact, for nontrivial ranges of parameters this convergence is fast. Moreover, the set of fixed points of the dynamics form a nontrivial class of networks. For the static game, we give classes of efficient networks for nontrivial parameter ranges and further study their stability. We close several problems, and leave many interesting ones open.