The key highlights and insights from the content are:
Motivation: When a new product enters a market already dominated by an existing product, it faces the challenge of surviving and gaining market share. The paper aims to address this problem by identifying an optimal set of users to target with advertisements and form a community that can help the new product establish a positive market share.
System Model: The authors model the competition between the new product (Product 2) and the existing dominant product (Product 1) using the bi-SIS (Susceptible-Infected-Susceptible) epidemic model. They introduce the concept of a "community" where a subset of users actively engage and influence each other, thereby increasing the spread of the new product.
Problem Formulation: The authors formulate an optimization problem to maximize the market share of the new product (Product 2) under a given budget constraint. The problem involves determining the optimal set of users to target and the level of investment in the community (captured by the parameter γ).
Analysis: The authors employ a perturbation-based approach to analyze the sensitivity of the new product's market share with respect to the targeted users. They establish a key result that the increase in market share is roughly proportional to the Perron-Frobenius eigenvector of the modified adjacency matrix, which captures the influence of the targeted users.
Optimization and Heuristic: The authors define an optimization problem to find the locally optimal set of users to target, given the budget constraint. They also propose a heuristic algorithm to solve this problem efficiently.
Experimental Evaluation: The authors evaluate their approach using real-world social network datasets and compare it against baseline methods, such as centrality-based measures and the NetShield algorithm. The results demonstrate that the proposed approach outperforms the baselines in terms of the new product's market share, under both homogeneous and heterogeneous cost distributions.
Overall, the paper presents a novel approach to help a new product establish a positive market share in a competitive environment by strategically forming a community of targeted users and leveraging their influence.
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arxiv.org
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