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We Can't Disagree Forever

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Author Info
John Geanakoplos () (Cowles Foundation, Yale University)
Heracles M. Polemarchakis (Columbia University)
Abstract

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, 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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  1. Kata Bognar & Lones Smith, 2004. "We Can't Argue Forever," IEHAS Discussion Papers 0415, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
  2. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Lucie Ménager, 2004. "A note on consensus and common knowledge of an aggregate of decisions," Cahiers de la Maison des Sciences Economiques v04006, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
  4. MINELLI, Enrico & POLEMARCHAKIS, Heracles, 2000. "Information at equilibrium," CORE Discussion Papers 2000004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  5. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation, Yale University. [Downloadable!]
  6. Wolfgang Pesendorfer & Faruk Gul, 2007. "The Canonical Space for Behavioral Types," Levine's Bibliography 843644000000000345, UCLA Department of Economics. [Downloadable!]
  7. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science. [Downloadable!]
  8. Vieille, Nicolas & Rosenberg, Dinah & Solan, Eilon, 2006. "Informational externalities and convergence of behavior," Les Cahiers de Recherche 856, HEC Paris. [Downloadable!]
  9. Peter Thompson & Steven Klepper, 2006. "Intra-Industry Spinoffs," Working Papers 0605, Florida International University, Department of Economics. [Downloadable!]
  10. David E. Bloom & Christopher L. Cavanagh, 1987. "Negotiator Behavior Under Arbitration," NBER Working Papers 2211, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Nicolas Houy & Lucie Ménager, 2005. "Communication, consensus and order. Who wants to speak first ?," Cahiers de la Maison des Sciences Economiques v05030, Université Panthéon-Sorbonne (Paris 1), revised Jan 2006. [Downloadable!]
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  12. Lucie Ménager, 2005. "Consensus, Communication and Knowledge : an Extension with Bayesian Agents," Cahiers de la Maison des Sciences Economiques v05031, Université Panthéon-Sorbonne (Paris 1), revised Jan 2006. [Downloadable!]
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  13. James Bergin, 1986. "We Eventually Agree," Discussion Papers 710, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  14. Frederic Koessler, 2000. "Common Knowledge and Consensus with Noisy Communication," Econometric Society World Congress 2000 Contributed Papers 0887, Econometric Society. [Downloadable!]
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  15. Hellman, Ziv, 2007. "Common Knowledge and Disparate Priors: When it is O.K. to Agree to Disagree," MPRA Paper 3404, University Library of Munich, Germany. [Downloadable!]
  16. Rajiv Sethi & Muhamet Yildiz, 2009. "Public Disagreement," Economics Working Papers 0089, Institute for Advanced Study, School of Social Science. [Downloadable!]
  17. Galanis, Spyros, . "Unawareness of Theorems," Discussion Paper Series In Economics And Econometrics 0709, Economics Division, School of Social Sciences, University of Southampton. [Downloadable!]
  18. Oscar Volij, 1997. "Communication, Credible Improvements and the Core of an Economy with Asymmetric Information," Game Theory and Information 9711001, EconWPA. [Downloadable!]
  19. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany. [Downloadable!]
  20. Zwiebel, Jeffrey H. & Vayanos, Dimitri & DeMarzo, Peter M., 2001. "Persuasion Bias, Social Influence, and Uni-Dimensional Opinions," Research Papers 1719, Stanford University, Graduate School of Business. [Downloadable!]
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