# A Model for Information Networks: Efficiency, Stability and Dynamics

## TL;DR

This paper introduces a simple directed network model inspired by social media, analyzing its stability, efficiency, and the emergence of natural social network structures through dynamic and static game approaches.

## Contribution

It develops a novel network model with non-substitutable edges, proves convergence to stable networks, and characterizes the structures that emerge under various parameters.

## Key findings

- Asynchronous dynamics converge quickly to stable networks.
- Stable networks can exhibit community and broadcast structures.
- The model captures diverse social network formations.

## Abstract

We introduce a simple network model that is inspired by social information networks such as twitter. Agents are nodes, connecting to another agent by building a directed edge has a cost, and reaching 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. Even in its simplest form, edges in this framework are neither substitutes or complements in general; hence, standard techniques are required to study the model's properties and dynamics do not apply. We prove that an asynchronous edge dynamics always converge to a stable network; in fact, for this convergence is fast for a range of parameters. Moreover, the set of stable networks are nontrivial and can support the type of network structures that have been observed to appear in social information networks -- from community clusters to broadcast networks, depending on the parameters many natural formations can emerge. We further study the static game, and give classes of stable and efficient networks for nontrivial parameter ranges. We close several problems, and leave many interesting ones open.