Branching Process with Attack: Viral Competing Markets

TL;DR

This paper introduces a new branching process model with attack dynamics to analyze competing viral content spread on social networks, revealing conditions for coexistence or extinction of posts.

Contribution

It develops a novel branching process with attack framework and derives conditions for coexistence and extinction in competing viral markets.

Findings

Either one or both posts go extinct or coexist at equilibrium.

Derived asymptotic ratios of competing populations.

Insights into seed user number and post quality effects.

Abstract

The marked increase in advertisements over online social networks (OSNs) necessitates the study of content propagation. We analyse the viral markets with content providers competing for the propagation of similar posts over OSNs. Towards this, we required a new variant of the branching process (BP), which we named as "Branching process with attack"; the entities upon wake up attempt to attack and acquire the opposite population; furthermore, each entity produces its offsprings as is usually considered in BPs. In addition to providing expressions for the growth rates of individual posts, dichotomy etc., we explore the co-existence of posts; can the competing content spread and explode (number of unread/live copies of both posts grow significantly with time) simultaneously over the network? We prove that either one or both populations/posts get extinct or the populations settle to a unique co-existence equilibrium and derive the corresponding asymptotic ratios of the two populations/posts. Our analysis applies to large population networks focusing on mass behaviour, rather than micro details. Our study provides insights into two crucial design aspects, the number of seed users and the quality of the post.