Cheap Talk Games with Sequential Posterior Formation

Abstract

People often have to acquire information from sources who may not share their preferences. This work studies the behavior of economic agents who face this situation through cheap talk games, where a potentially un-aligned sender communicates information about the state of the world to a receiver. In our model, the receiver exhibits a specific type of irrationality called sequential updating. Rather than directly using Bayes' Rule to form beliefs about the state of the world, this receiver first forms a belief about the sender's motivation based on their message and then uses that belief to determine the state. This behavior over-emphasizes the sender's motivation and leads the receiver to con rm their own priors by using the same message to update them twice. We show in three cheap talk contexts that, compared to the original Bayesian formulations, introducing sequentially-updating receivers does not dramatically alter the form of equilibrium or the receiver's expected utility. However, we identify a clear effect that depends on the sender's bias: sequential updating curtails the effects of misleading messages by un-aligned senders, but at the cost of making the receiver less responsive to the truth. By extending sequential updating from a non-strategic context to a game theoretic one, we showcase its strengths in producing realistic responses and also its weaknesses, in particular the complex conditions it induces. We also propose extensions of this paradigm to network models of communication which more accurately capture large-scale behavior in the face of potential misinformation.