[UTMD-066] Dynamics of Common Beliefs and the Value of Communication (by Konan Shimizu)

Konan Shimizu

We analyze the evolution of common beliefs among two agents, where one agent (the informed) knows the true state while the other (the uninformed) learns the true state over T periods via i.i.d. private signals. We examine how information sharing among them affects the emergence of common beliefs. Information sharing is assumed to be non-strategic and imperfect in the sense that it imperfectly reveals the signals received by the uninformed agent. We define the value of information sharing as (the probability that the true state is common p-believed under information sharing) – (the probability under no information sharing), and we show that the value of information sharing depends on T (how long the uninformed agent learns). Intuitively, information sharing appears to help achieve common beliefs, but this is only true when T is small. The value of information sharing is positive for small T, but it becomes negative when T is larger. Moreover, the value of information sharing can be equal to zero for all sufficiently large values of T, and we provide almost necessary and sufficient conditions for this to hold.