Maximizing Influence in Competitive Environments: A Game-Theoretic Approach

Ideas, ranging from product preferences to political views, spread through social interactions. These interactions may determine how ideas are adopted within a market and which, if any, become dominant. In this paper, we introduce a model for Dynamic Influence in Competitive Environments (DICE). We show that existing models of influence propagation, including linear threshold and independent cascade models, can be derived as special cases of DICE. Using DICE, we explore two scenarios of competing ideas, including the case where a newcomer competes with a leader with an already-established idea, as well as the case where multiple competing ideas are introduced simultaneously. We formulate the former as a Stackelberg game and the latter as a simultaneous-move game of complete information. Moreover, we show that, in both cases, the payoff functions for both players are submodular, leading to efficient algorithms for each player to approximate his optimal strategy. We illustrate our approach using the Wiki-vote social network dataset.