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. Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related " no trade " condition likewise provides a characterization of feasibility . We use our characterization to study joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
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 due to Dawid et al. (1995). 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.
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Our main result is that, for the two agent case,
For two agents we introduce
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provides a necessary and sufficient condition for feasibility.
, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995).
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a related
we characterize feasible distributions in terms of a
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no trade
no-trade
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likewise provides a characterization of feasibility
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our characterization to study joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian
these characterizations to study information structures with independent posteriors. We also study
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a single sender and
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and explore the extreme points of the set of
exploring the extreme