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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.

Suggested Citation

  • John Geanakoplos, 1989. "Game Theory Without Partitions, and Applications to Speculation and Consensus," Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:914
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d09/d0914.pdf
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    1. 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.
    2. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    3. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
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    Citations

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    Cited by:

    1. Marks, Robert, 1998. "Evolved perception and behaviour in oligopolies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1209-1233, August.
    2. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    3. 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.
    4. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    5. Ortoleva, Pietro, 2013. "The price of flexibility: Towards a theory of Thinking Aversion," Journal of Economic Theory, Elsevier, vol. 148(3), pages 903-934.
    6. Marco Scarsini & Yossi Feinberg, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-12.
    7. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    8. Galanis, Spyros, 2016. "The value of information in risk-sharing environments with unawareness," Games and Economic Behavior, Elsevier, vol. 97(C), pages 1-18.
    9. 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.
    10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    11. Proto, Eugenio & Sgroi, Daniel, 2017. "Biased beliefs and imperfect information," Journal of Economic Behavior & Organization, Elsevier, vol. 136(C), pages 186-202.
    12. 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.
    13. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    14. 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.
    15. Jihong Lee, 2008. "Unforeseen Contingency and Renegotiation with Asymmetric Information," Economic Journal, Royal Economic Society, vol. 118(528), pages 678-694, April.
    16. Galanis, Spyros, 2015. "The value of information under unawareness," Journal of Economic Theory, Elsevier, vol. 157(C), pages 384-396.
    17. repec:ebl:ecbull:v:4:y:2003:i:11:p:1-12 is not listed on IDEAS
    18. 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.
    19. Gossner, Olivier & Tsakas, Elias, 2007. "Testing Rationality on Primitive Knowledge," Working Papers in Economics 275, University of Gothenburg, Department of Economics.
    20. 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.
    21. Liu Zhen, 2008. "The Dirty Face Problem with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-20, December.
    22. 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).
    23. repec:eee:matsoc:v:87:y:2017:i:c:p:11-21 is not listed on IDEAS

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