Influence Propagation in Competitive Scenario: Winning with Least Amount of Investment in Separated Threshold Model

In a market environment, there often are multiple vendors offering similar products or services. It has been observed that individuals' decisions to adopt a product or service are influenced by the recommendations of their friends and acquaintances. Consequently, in the last few years there has been considerable interest in the research community to study the dynamics of influence propagation in social networks in competitive settings. The goal of these studies is often to identify the key individuals in a social network, whose recommendations have significant impact on adoption of a product or service by the members of that community. Using Separated Threshold Model (SepT) [1] of influence propagation, in this paper we study a problem of similar vein, where the goal of the two vendors (players) is to win the competition by having a market share that is larger than its competitor. In our model, the first player has already identified a set of key influencers when the second player enters the market. The goal of the second player is to have a larger market share, but wants to achieve the goal with least amount of investment, i.e., by incentivizing the fewest number of key individuals (influencers) in the social network. The problem is NP-hard. We provide an approximation algorithm with O(log n) bound. Detailed experimentations have been conducted to evaluate the efficacy of our algorithm. Moreover, we present an equivalent random process for the SepT model which facilitates analysis of competitive influence propagation under this model.