A game-theoretic model of misinformation spread on social networks

In this paper, we develop a game-theoretic model of sharing decisions among users of a Twitter-like social network. Agents have a subjective prior on an unobservable real-valued state, representing their beliefs on a topic that is subject to a binary action. Agents cast their binary action, matching the sign of the state. Before the action stage, a small fraction of agents receive a piece of news which impacts their beliefs. Those who receive the news update their belief and make a decision as to whether to share the news with their followers in order to influence their beliefs, and in turn their actions, given a fixed cost for sharing. We characterize the underlying news spread as an endogenous Susceptible-Infected (SI) epidemic process and derive agents' sharing decisions as well as the size of the sharing cascade at the equilibrium of the game. We show that lower credibility news can result in a larger cascade than fully credible news provided that the network connectivity surpasses a connectivity limit. We further delineate the relationship between cascade size, network connectivity, and news credibility in terms of polarization and diversity in prior beliefs: We demonstrate that increased polarization reduces the connectivity limit whereas larger in-party diversity has a non-monotone effect on the connectivity limit, which depends on both the levels of polarization and in-party diversity. Our results provide a theoretical foundation for recent empirical observations demonstrating faster and wider spread of low-credibility and false information on social networks.