Competitive Propagation: Models, Asymptotic Behavior and Multi-stage Games

TL;DR

This paper introduces a class of models for competing product propagation over social networks, analyzing their asymptotic behavior, and proposing multi-stage game strategies for resource allocation and seeding.

Contribution

It develops novel propagation models incorporating social and self conversions, introduces the product-conversion graph, and analyzes multi-stage competitive games with Nash equilibrium insights.

Findings

Asymptotic behavior depends on network and product-conversion graph structures.

Independence approximation is validated through numerical analysis.

Nash equilibrium strategies are characterized for multi-stage propagation games.

Abstract

In this paper we propose a class of propagation models for multiple competing products over a social network. We consider two propagation mechanisms: social conversion and self conversion, corresponding, respectively, to endogenous and exogenous factors. A novel concept, the product-conversion graph, is proposed to characterize the interplay among competing products. According to the chronological order of social and self conversions, we develop two Markov-chain models and, based on the independence approximation, we approximate them with two respective difference equations systems. Theoretical analysis on these two approximation models reveals the dependency of the systems' asymptotic behavior on the structures of both the product-conversion graph and the social network, as well as the initial condition. In addition to the theoretical work, accuracy of the independence approximation and the asymptotic behavior of the Markov-chain model are investigated via numerical analysis, for the case where social conversion occurs before self conversion. Finally, we propose a class of multi-player and multi-stage competitive propagation games and discuss the seeding-quality trade-off, as well as the allocation of seeding resources among the individuals. We investigate the unique Nash equilibrium at each stage and analyze the system's behavior when every player is adopting the policy at the Nash equilibrium.