A Two Phase Investment Game for Competitive Opinion Dynamics in Social Networks

We study the problem of two competing camps aiming to maximize the adoption of their respective opinions, by optimally investing in nodes of a social network in two phases. The final opinion of a node in phase 1 acts as its bias in phase 2, and this bias determines the effectiveness of a camp’s investment on the node. Using an extension of Friedkin-Johnsen model of opinion dynamics, we formulate the camps’ utility functions. We show the existence and polynomial time computability of Nash equilibrium under reasonable assumptions. Using simulations, we quantify the effects of the nodes’ biases and the weightage attributed to them, as well as that of a camp deviating from its equilibrium strategy.