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We Can't Disagree Forever


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    Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will converge to a common equilibrium posterior, even though they may base their posteriors on quite different information. Furthermore, given any integer, n, one can construct an example in which the revision process not only takes n steps to converge, but no evident revision occurs ñ for (n-1) steps both agents repeat the same conflicting posteriors ñ until the last step when the two agents decide to agree. Common knowledge of each other's posterior does not necessarily lead agents to the posterior they would have agreed upon had information been directly exchanged. On the other hand, the examples that are characterized by a discrepancy between the direct and indirect communication equilibrium are rare: with probability 1, the revision process constructed here leads the two agents in one step to the direct communication equilibrium.

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    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 639.

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    Length: 14 pages
    Date of creation: Jul 1982
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    Publication status: Published in Journal of Economic Theory (October 1982), 28(1): 192-200
    Handle: RePEc:cwl:cwldpp:639

    Note: CFP 552.
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    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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