Bayesian Conversations

We initiate the study of Bayesian conversations, which model interactive communication between two strategic agents without a mediator. We compare this to communication through a mediator and investigate the settings in which mediation can expand the range of implementable outcomes. We look into the eventual outcome of two-player games after interactive communication. We focus on games where only one agent has a non-trivial action and examine the performance of communication protocols that are individually rational (IR) for both parties. Our key findings reveal that for ex-ante IR the expected social welfare achievable through a mediator protocol are equivalent to that achievable through unmediated Bayesian conversations. For ex-post IR, we observe a gap in the achievable welfare of the two protocols. We also establish that the optimal welfare under ex-post IR Bayesian conversation may require infinitely many rounds of communication. Additionally, we provide characterizations of which distributions over posteriors are achievable via Bayesian conversations.