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. In the first part of the paper, we ask whether the distributions of posterior beliefs that can be induced by a mediator protocol can also be induced by a (unmediated) Bayesian conversation. We show this is not possible -- mediator protocols can ``correlate'' the posteriors in a way that unmediated conversations cannot. Additionally, we provide characterizations of which distributions over posteriors are achievable via mediator protocols and Bayesian conversations. In the second part of the paper, we delve deeper 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. We consider different levels of IR including ex-ante, interim, and ex-post; and we impose different restrictions on how Alice and Bob can deviate from the protocol: the players are committed/non-committed. Our key findings reveal that, in the cases of ex-ante and interim IR, the expected utilities achievable through a mediator are equivalent to those achievable through unmediated Bayesian conversations. However, in the models of ex-post IR and non-committed interim IR, we observe a separation in the achievable outcomes.

翻译：我们首次研究了贝叶斯对话，该模型描述了两个没有中介的战略主体之间的交互式沟通。我们将其与通过中介进行的沟通进行比较，并探讨了中介能够扩展可实现结果范围的条件。在论文的第一部分，我们探究了通过中介协议诱导的后验信念分布是否也能通过（无中介的）贝叶斯对话实现。结果表明这是不可能的——中介协议能以无中介对话无法实现的方式“关联”后验信念。此外，我们给出了通过中介协议和贝叶斯对话可实现的后验分布特征刻画。在论文的第二部分，我们深入探讨了交互式沟通后双人博弈的最终结果。我们聚焦于仅有一方持有非平凡行动集的博弈，分析了对双方都具有个体理性（IR）的沟通协议性能。我们考虑了不同层面的个体理性，包括事前、事中和事后；并对Alice和Bob偏离协议的方式施加了不同的限制：参与者承诺/不承诺。我们的核心发现表明：在事前和事中个体理性情形下，通过中介实现的期望效用与通过无中介贝叶斯对话实现的期望效用等价。然而，在事后个体理性和非承诺事中个体理性模型中，我们发现可实现结果存在差异。