Sufficient Conditions for Formation of a Network Topology by Self-interested Agents

TL;DR

This paper investigates the conditions under which self-interested agents form specific stable network topologies, such as stars or complete graphs, through recursive network formation models considering individual utilities and strategic link decisions.

Contribution

It introduces a recursive network formation model and derives sufficient conditions for the emergence of various desired network topologies as stable outcomes.

Findings

Identifies conditions for star, complete, and bipartite Turan graphs to be stable.

Analyzes social welfare implications of different stable topologies.

Provides a framework for understanding network formation among strategic agents.

Abstract

Networks such as organizational network of a global company play an important role in a variety of knowledge management and information diffusion tasks. The nodes in these networks correspond to individuals who are self-interested. The topology of these networks often plays a crucial role in deciding the ease and speed with which certain tasks can be accomplished using these networks. Consequently, growing a stable network having a certain topology is of interest. Motivated by this, we study the following important problem: given a certain desired network topology, under what conditions would best response (link addition/deletion) strategies played by self-interested agents lead to formation of a pairwise stable network with only that topology. We study this interesting reverse engineering problem by proposing a natural model of recursive network formation. In this model, nodes enter the network sequentially and the utility of a node captures principal determinants of network formation, namely (1) benefits from immediate neighbors, (2) costs of maintaining links with immediate neighbors, (3) benefits from indirect neighbors, (4) bridging benefits, and (5) network entry fee. Based on this model, we analyze relevant network topologies such as star graph, complete graph, bipartite Turan graph, and multiple stars with interconnected centers, and derive a set of sufficient conditions under which these topologies emerge as pairwise stable networks. We also study the social welfare properties of the above topologies.