Mathieu Faure: mathieu.faure[at]univ-amu.fr
Kenan Huremovic: kenan.huremovic[at]univ-amu.fr
We consider a linear threshold model of cascades in networks. An agent switches (e.g. adopts an innovation) if the proportion of his neighbors who have already switched exceeds his threshold. Agents’ thresholds are drawn randomly at the start of the cascade process. We present a result for the expected number of switches in arbitrary finite networks with any initial seeds. For certain network topologies, we find analytic expressions for the expected number of switches. We define a new measure of an agent’s ability to influence a cascade in a given network, called cascade centrality, which is the expected size of the cascade when the agent is the only seed in the network. We then consider a setting in which two firms compete to diffuse their products in a social network. Firm seed their products simultaneously and products diffuse according to the threshold model. Using cascade centrality, we provide a characterization of networks that admit pure-strategy Nash equilibria (PSNE). We provide tight bounds for the efficiency of these equilibria and for the inequality in firms’ equilibrium payoffs. In trees, PSNE always exists and can be efficiently found. Our simple model admits a variety of extensions.