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Keeping Up With the Winner! Targeted Advertisement to Communities in Social Networks

Shailaja Mallick, Vishwaraj Doshi, Do Young Eun

TL;DR

The paper tackles the problem of enabling a weaker product to survive a dominant rival on a social network by deploying targeted advertising to form a community. It adopts a bi-SIS diffusion framework and introduces a budget-constrained optimization that leverages a rank-one perturbation to the network adjacency via $\mathbf{A}+\gamma\mathbf{u}\mathbf{u}^T$, guiding where to allocate promotional effort. A key result is a perturbation-based, locally optimal selection rule: the gain in long-run market share $\bar{y}$ scales with the PF eigenvector component $\nu_i^c$ of the critical state, leading to a knapsack-like selection of users according to $\nu_i^c/w_i$. Empirical evaluation on real Facebook networks shows substantial improvements in $\bar{y}$ over standard centrality and NetShield baselines under both homogeneous and heterogeneous costs, highlighting a practical spectral-guided strategy for niche-targeted marketing to foster coexistence and positive market share.

Abstract

When a new product enters a market already dominated by an existing product, will it survive along with this dominant product? Most of the existing works have shown the coexistence of two competing products spreading/being adopted on overlaid graphs with same set of users. However, when it comes to the survival of a weaker product on the same graph, it has been established that the stronger one dominates the market and wipes out the other. This paper makes a step towards narrowing this gap so that a new/weaker product can also survive along with its competitor with a positive market share. Specifically, we identify a locally optimal set of users to induce a community that is targeted with advertisement by the product launching company under a given budget constraint. To this end, we model the system as competing Susceptible-Infected-Susceptible (SIS) epidemics and employ perturbation techniques to quantify and attain a positive market share in a cost-efficient manner. Our extensive simulation results with real-world graph dataset show that with our choice of target users, a new product can establish itself with positive market share, which otherwise would be dominated and eventually wiped out of the competitive market under the same budget constraint.

Keeping Up With the Winner! Targeted Advertisement to Communities in Social Networks

TL;DR

The paper tackles the problem of enabling a weaker product to survive a dominant rival on a social network by deploying targeted advertising to form a community. It adopts a bi-SIS diffusion framework and introduces a budget-constrained optimization that leverages a rank-one perturbation to the network adjacency via , guiding where to allocate promotional effort. A key result is a perturbation-based, locally optimal selection rule: the gain in long-run market share scales with the PF eigenvector component of the critical state, leading to a knapsack-like selection of users according to . Empirical evaluation on real Facebook networks shows substantial improvements in over standard centrality and NetShield baselines under both homogeneous and heterogeneous costs, highlighting a practical spectral-guided strategy for niche-targeted marketing to foster coexistence and positive market share.

Abstract

When a new product enters a market already dominated by an existing product, will it survive along with this dominant product? Most of the existing works have shown the coexistence of two competing products spreading/being adopted on overlaid graphs with same set of users. However, when it comes to the survival of a weaker product on the same graph, it has been established that the stronger one dominates the market and wipes out the other. This paper makes a step towards narrowing this gap so that a new/weaker product can also survive along with its competitor with a positive market share. Specifically, we identify a locally optimal set of users to induce a community that is targeted with advertisement by the product launching company under a given budget constraint. To this end, we model the system as competing Susceptible-Infected-Susceptible (SIS) epidemics and employ perturbation techniques to quantify and attain a positive market share in a cost-efficient manner. Our extensive simulation results with real-world graph dataset show that with our choice of target users, a new product can establish itself with positive market share, which otherwise would be dominated and eventually wiped out of the competitive market under the same budget constraint.
Paper Structure (16 sections, 6 theorems, 32 equations, 8 figures, 1 table, 2 algorithms)

This paper contains 16 sections, 6 theorems, 32 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Setup
  3. The System Model
  4. Problem Setup
  5. Analysis of Product 2's Market share $\bar{y}$
  6. Minimum Budget for $\bar{y}>0$
  7. Main Result
  8. Experimental Setup & Results
  9. Simulation Setup
  10. Comparison with Baseline Methodologies
  11. Simulation Results
  12. Conclusion & Future Work
  13. Appendix
  14. Proof of Proposition \ref{['prop::budget equality']}
  15. Proof of Lemma \ref{['lemma::initial_candidate']}
  16. ...and 1 more sections

Key Result

Proposition 3.1

Any solution $(\gamma^*,\mathbf{u}^*)$ to the optimization problem op:maximize y always satisfies the budget constraint with equality, that is,

Figures (8)

  • Figure 1: Real web-search percentage over a time period showing the introduction of a new product (Galaxy S4 & Xbox 360) alongside an existing product (iPhone 4S & PlayStation 2).
  • Figure 2: Illustration of users forming community (Nodes 1,3,6-8 in layer $\mathcal{F}$). The blue (red) nodes denote users adopting Product 1 (Product 2) at any given instance, and gray nodes are the users who do not own any of the products.
  • Figure 3: Heat map illustration of the market share as a function of budget $C$ and $\bar{x}^*$.
  • Figure 4: Facebook ($\approx4k$ nodes): Change in $\bar{\mathbf{y}}$ (AvgY) and $\bar{\mathbf{x}}$ (AvgX) for Homogeneously distributed cost and different values of $\epsilon$.
  • Figure 5: Facebook ($\approx4k$ nodes): Change in $\bar{\mathbf{y}}$ (AvgY) and $\bar{\mathbf{x}}$ (AvgX) for Heterogeneously distributed cost and different values of $\epsilon$.
  • ...and 3 more figures

Theorems & Definitions (12)

  • Proposition 3.1
  • Lemma 3.2
  • Theorem 3.3
  • proof
  • proof
  • Lemma A.1
  • proof
  • Lemma A.2
  • proof
  • Proposition A.3
  • ...and 2 more