We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, we introduce a quantitative version of Aumann’s agreement theorem and show that it is equivalent to a characterization of feasible distributions from a 1995 work by Dawid and colleagues. For any number of agents, we characterize feasible distributions in terms of a “no-trade” condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

中文翻译：

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可行的联合后验信念

我们研究了一组代理的可能联合后验置信分布集，这些代理共享关于二元状态的共同先验并观察一些信息结构。对于两个智能体，我们引入了 Aumann 一致性定理的定量版本，并表明它等效于 Dawid 及其同事 1995 年工作中的可行分布的表征。对于任意数量的代理，我们根据“无交易”条件表征可行分布。我们使用这些特征来研究具有独立后验的信息结构。我们还研究了多个接收者的说服问题，探索了极端可行的分布。