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：我们开始研究贝叶斯对话，该模型描述了两位策略型主体在没有中介者情况下的交互式通信。我们将此与通过中介者的通信进行比较，并探讨中介能够扩大可实现结果范围的情境。论文第一部分探究：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）贝叶斯对话诱导。研究表明答案是否定的——中介协议能以无中介对话无法实现的方式“关联”后验分布。此外，我们给出了中介协议与贝叶斯对话可实现后验分布的表征。论文第二部分深入分析交互式通信后两人博弈的最终结果。我们聚焦于仅有一位主体具有非平凡行动的博弈，考察对双方均满足个体理性（IR）的通信协议性能。我们考虑不同层级的IR，包括事前、临时与事后IR；并对艾丽斯与鲍勃偏离协议的方式施加不同限制：主体可为承诺型/非承诺型。关键发现表明：在事前与临时IR情形下，通过中介实现的事前期望效用与无中介贝叶斯对话可实现的效用等价。但在事后IR与非承诺临时IR模型中，观察到可实现结果存在分离现象。