Competitive Contagion with Sparse Seeding

TL;DR

This paper models competitive product diffusion in social networks, showing how firms can strategically seed key individuals to optimize market share with sparse seeding strategies influenced by network structure.

Contribution

Introduces a novel framework for sparse seeding in a duopoly game, analyzing how network structure affects optimal seeding strategies and their sparsification.

Findings

Sparse seeding can be an equilibrium strategy in large populations.

Network structure significantly influences seeding strategies.

Near Nash equilibrium strategies can lead to sparse seeding asymptotically.

Abstract

This paper studies a strategic model of marketing and product diffusion in social networks. We consider two firms offering substitutable products which can improve their market share by seeding the key individuals in the market. Consumers update their consumption level for each of the two products as the best response to the consumption of their neighbors in the previous period. This results in linear update dynamics for the product consumption. Each consumer receives externality from the consumption of each neighbor where the strength of the externality is higher for consumption of the products of the same firm. We represent the above setting as a duopoly game between the firms and introduce a novel framework that allows for sparse seeding to emerge as an equilibrium strategy. We then study the effect of the network structure on the optimal seeding strategies and the extent to which the strategies can be sparsified. In particular, we derive conditions under which near Nash equilibrium strategies can asymptotically lead to sparse seeding in large populations. The results are illustrated using a core-periphery network.