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Unawareness, Beliefs and Games

Author

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  • Heifetz, Aviad
  • Meier, Martin
  • Schipper, Burkhard C.

Abstract

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We use our unawareness belief structure to show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized “No-trade†theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the “No-agreeing-to-disagree†theorem.

Suggested Citation

  • Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2007. "Unawareness, Beliefs and Games," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 196, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    • Handle: RePEc:trf:wpaper:196
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    References listed on IDEAS

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    1. Burkhard C. Schipper & Martin Meier & Aviad Heifetz, 2007. "Unawareness, Beliefs and Games," Working Papers 235, University of California, Davis, Department of Economics.
    2. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    3. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    4. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    5. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
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    Citations

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    Cited by:

    1. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    2. 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.
    3. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
    4. Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
    5. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
    6. Oliver Board, 2008. "Object-Based Unawareness: Theory and Applications," Working Paper 378, Department of Economics, University of Pittsburgh, revised Mar 2009.
    7. Burkhard C. Schipper & Martin Meier & Aviad Heifetz, 2007. "Unawareness, Beliefs and Games," Working Papers 235, University of California, Davis, Department of Economics.
    8. Yi-Chun Chen & Jeffrey Ely & Xiao Luo, 2012. "Note on unawareness: Negative Introspection versus AU Introspection (and KU Introspection)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 325-329, May.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2007. "Unawareness, Beliefs and Games," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 196, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    10. Filiz-Ozbay, Emel, 2012. "Incorporating unawareness into contract theory," Games and Economic Behavior, Elsevier, vol. 76(1), pages 181-194.
    11. Andreas Blume & Uri Gneezy, 2009. "Cognitive Forward Induction and Coordination without Common Knowledge: An Experimental Study," Working Paper 346, Department of Economics, University of Pittsburgh, revised May 2009.
    12. Mengel, F. & Tsakas, E. & Vostroknutov, A., 2009. "Awareness in repeated games," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. Salvatore Modica, 2008. "Unawareness, priors and posteriors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 81-94, November.
    14. Halpern, Joseph Y. & Pass, Rafael, 2015. "Algorithmic rationality: Game theory with costly computation," Journal of Economic Theory, Elsevier, vol. 156(C), pages 246-268.

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    More about this item

    Keywords

    unawareness; awareness; type-space; Bayesian games; incomplete information; equilibrium; common prior; agreement; speculative trade; interactive epistemology;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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