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Game Theory Without Partitions, and Applications to Speculation and Consensus

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    Abstract

    Decision theory and game theory are extended to allow for information processing errors. This extended theory is then used to reexamine market speculation and consensus, both when all actions (opinions) are common knowledge and when they may not be. Five axioms of information processing are shown to be especially important to speculation and consensus. They are called nondelusion, knowing that you know, nested, balanced, and positively balanced. We show that it is necessary and sufficient that each agent's information processing errors be nondeluded and (1) balanced so that the agents cannot agree to disagree, (2) positively balanced so that it cannot be common knowledge that they are speculating, and (3) KTYK and nested so that agents cannot speculate in equilibrium. Each condition is strictly weaker than the next one, and the last is strictly weaker than partition information.

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    File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0914.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 914.

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    Length: 33 pages
    Date of creation: May 1989
    Date of revision:
    Handle: RePEc:cwl:cwldpp:914

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

    Related research

    Keywords: Game theory; decision theory; speculation; consensus; information; common knowledge;

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    1. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    2. Dubey, Pradeep & Geanakoplos, John & Shubik, Martin, 1987. "The revelation of information in strategic market games : A critique of rational expectations equilibrium," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 105-137, April.
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    Cited by:
    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Unawareness, Beliefs and Speculative Trade," MPRA Paper 18437, University Library of Munich, Germany.
    2. Kawamura, Enrique, 2004. "Investors's distrust and the marketing of new financial assets," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 265-295, May.
    3. Robert E. Marks, . "Evolved Perception and Behaviour in Oligopolies," Computing in Economics and Finance 1996 _038, Society for Computational Economics.
    4. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    5. Gossner, Olivier & Tsakas, Elias, 2007. "Testing Rationality on Primitive Knowledge," Working Papers in Economics 275, University of Gothenburg, Department of Economics.
    6. Blume, Andreas & Gneezy, Uri, 2010. "Cognitive forward induction and coordination without common knowledge: An experimental study," Games and Economic Behavior, Elsevier, vol. 68(2), pages 488-511, March.
    7. repec:ebl:ecbull:v:4:y:2003:i:11:p:1-12 is not listed on IDEAS
    8. Jihong Lee, 2007. "Unforeseen Contingency and Renegotiation with Asymmetric Information," Birkbeck Working Papers in Economics and Finance 0717, Birkbeck, Department of Economics, Mathematics & Statistics.
    9. Frédéric KOESSLER, 2002. "Strategic Knowledge Sharing in Bayesian Games: A General Model," Working Papers of BETA 2002-01, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    10. Tsakas, Elias & Voorneveld, Mark, 2011. "On consensus through communication without a commonly known protocol," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 733-739.
    11. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    12. Luo, Xiao & Ma, Chenghu, 2003. ""Agreeing to disagree" type results: a decision-theoretic approach," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 849-861, November.
    13. Gossner Olivier & Tsakas Elias, 2010. "A reasoning approach to introspection and unawareness," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Dekel, Eddie & Lipman, Barton L. & Rustichini, Aldo, 1998. "Recent developments in modeling unforeseen contingencies," European Economic Review, Elsevier, vol. 42(3-5), pages 523-542, May.
    15. Marco Scarsini & Yossi Feinberg, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-12.

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