False Information from Near and Far

We study the transmission of messages in social networks in the presence of biased and unbiased
agents. Biased agents prefer a specific outcome while unbiased agents prefer the true state of the world. Each agent who receives a message knows the identity (but not the type) of the person from whom the message originates and only the identity and types of their immediate neighbors. After learning the true state of the world, depending on their type, the root agent creates and transmit a message about the state to her neighbors who may then decide to transmit it forward depending on their type. We characterize the perfect Bayesian equilibria of the game, and show that the social network acts as a filter: distance between the source and the other agents who form posteriors beliefs about the true state based on the message received now depends on the distance a message travels. Thus, unbiased agents, who receive a message from a biased agent, are more likely to transmit it further by assigning higher credibility to it when they are further away from the source. For a given network, we compute the probability that it will always support the transmission of messages by biased agents. We establish that star networks maximize the probability that messages will be transmitted. Finally, we establish that under some parameters, this probability increases when agents have uncertainty about their location in the network.