False Information from Near and Far

We study message credibility in social networks with 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 type) of the message creator and only the identity and types of their immediate neighbors. We characterize the perfect Bayesian equilibria of this game and demonstrate filtering by the network: the posterior beliefs of agents depend on the distance a message travels. Unbiased agents, who receive a message from a biased agent, are more likely to assign a higher credibility and transmit it further when they are further away from the source. For a given network, we compute the probability that it will always support the communication of messages by unbiased agents. Finally, we establish that under certain parameters, this probability increases when agents are uncertain about their network location.