Competitive Influence Maximization: Integrating Budget Allocation and Seed Selection

Abstract: Today, many companies take advantage of viral marketing to promote their new products, and since there are several competing companies in many markets, Competitive Influence Maximization has attracted much attention. Two categories of studies exist in the literature. First, studies that focus on which nodes from the network to select considering the existence of the opponents. Second, studies that focus on the problem of budget allocation. In this work, we integrate these two lines of research and propose a new scenario where competition happens in two phases. First, parties identify the most influential nodes of the network. Then they compete over only these influential nodes by the amount of budget they allocate to each node. We provide a strong motivation for this integration. Also, in previous budget allocation studies, any fraction of the budget could be allocated to a node, which means that the action space was continuous. However, in our scenario, we consider that the action space is discrete. This consideration is far more realistic, and it significantly changes the problem. We model the scenario as a game and propose a novel framework for calculating the Nash equilibrium. Notably, building an efficient framework for this problem with such a huge action space and also handling the stochastic environment of influence maximization is very challenging. To tackle these difficulties, we devise a new payoff estimation method and a novel best response oracle to boost the efficiency of our framework. Also, we validate each aspect of our work through extensive experiments.