Network Formation: Heterogeneous Traffic, Bilateral Contracting and Myopic Dynamics

TL;DR

This paper analyzes a network formation game with heterogeneous traffic, bilateral contracting, and myopic dynamics, characterizing stable topologies, their convergence, and computational complexity.

Contribution

It extends previous models by allowing non-uniform traffic demands and studies stability, convergence, and complexity of network topologies.

Findings

Stable topologies are characterized under static analysis.

Myopic dynamics converge to stable networks under certain conditions.

Deciding the existence of stable topologies with a given price is NP-complete.

Abstract

We study a network formation game where nodes wish to send traffic to other nodes. Nodes can contract bilaterally other nodes to form bidirectional links as well as nodes can break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the model considered in Arcaute et al. The novelty is that we do no require the traffic to be uniform all-to-all. Each node specifies the amount of traffic that it wants to send to any other node. We characterize stable topologies under a static point of view and we also study the game under a myopic dynamics. We show its convergence to stable networks under some natural assumptions on the contracting functions. Finally we consider the efficiency of pairwise Nash topologies from a social point of view and we show that the problem of deciding the existence stable topologies of a given price is $\NP$-complete.