Competitive Propagation: Models, Asymptotic Behavior and Multi-stage Games
Wenjun Mei, Francesco Bullo

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…
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Taxonomy
TopicsOpinion Dynamics and Social Influence · Complex Network Analysis Techniques · Game Theory and Applications
