Competitive Rumor Spread in Social Networks.

We consider a setting in which two firms compete to spread rumors in a social network. Firms seed their rumors simultaneously and rumors propagate according to the linear threshold model. Consumers have (randomly drawn) heterogeneous thresholds for each product. Using the concept of cascade centrality introduced by [6], we provide a sharp characterization of networks in which games admit purestrategy Nash equilibria (PSNE). We provide tight bounds for the efficiency of these equilibria and for the inequality in firms' equilibrium payoffs. When the network is a tree, the model is particularly tractable.