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Games with Unawareness

  • Feinberg, Yossi

    (Stanford University)

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    We provide a tool to model and solve strategic situations where players' perceptions are limited, in the sense that they may only be aware of, or model, some of the aspects of the strategic situations at hand, as well as situations where players realize that other players' perceptions may be limited. We define normal, repeated, incomplete information and dynamic (extensive) form games with unawareness using a unified methodology. A game with unawareness is defined as a collection of standard games (of the corresponding form). The collection specifies how each player views the game, how she views the other players' perceptions of the game and so on. The modeler's description of perceptions, the players' description of other players' reasoning, etc. are shown to have consistent representations. We extend solution concepts such as rationalizability and Nash equilibrium to these games and study their properties. It is shown that while unawareness in normal form games can be mapped to incomplete information games, the extended Nash equilibrium solution is not mapped to a known solution concept in the equivalent incomplete information games, implying that games with unawareness generate novel types of behavior.

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    File URL: https://gsbapps.stanford.edu/researchpapers/library/RP2122.pdf
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    Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 2122.

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    Date of creation: Aug 2012
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    Handle: RePEc:ecl:stabus:2122
    Contact details of provider: Postal: Stanford University, Stanford, CA 94305-5015
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    Web page: http://gsbapps.stanford.edu/researchpapers/
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    1. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    2. Martin Meier & Burkhard C. Schipper & Aviad Heifetz, 2009. "Dynamic Unawareness and Rationalizable Behavior," Working Papers 910, University of California, Davis, Department of Economics.
    3. Grant, Simon & Kline, Jeff & Quiggin, John, 2012. "Differential awareness, ambiguity, and incomplete contracts: a model of contractual disputes," Risk and Sustainable Management Group Working Papers 151200, University of Queensland, School of Economics.
    4. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2007. "Unawareness, Beliefs and Games," Bonn Econ Discussion Papers bgse6_2007, University of Bonn, Germany.
    5. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    6. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    8. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
    9. 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).
    10. Xiaojian ZHAO, . "Framing Contingencies in Contracts," EcoMod2008 23800158, EcoMod.
    11. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2005. "A Canonical Model for Interactive Unawareness," Bonn Econ Discussion Papers bgse23_2005, University of Bonn, Germany.
    12. Grant, Simon & Quiggin, John, 2012. "Inductive Reasoning About Unwareness," Risk and Sustainable Management Group Working Papers 151202, University of Queensland, School of Economics.
    13. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer, vol. 41(1), pages 131-155, February.
    14. Feinberg, Yossi, 2004. "Subjective Reasoning--Games with Unawareness," Research Papers 1875, Stanford University, Graduate School of Business.
    15. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    16. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
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