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Games with Unawareness

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  • Feinberg, Yossi

    (Stanford University)

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    Abstract

    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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    Bibliographic Info

    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

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    1. 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).
    2. Grant, Simon & Quiggin, John, 2009. "Inductive Reasoning About Unwareness," Risk and Sustainable Management Group Working Papers 151188, University of Queensland, School of Economics.
    3. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
    4. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Dynamic Unawareness and Rationalizable Behavior," MPRA Paper 15058, University Library of Munich, Germany.
    6. Grant, Simon & Kline, J. Jude & Quiggin, John, 2012. "Differential awareness, ambiguity, and incomplete contracts: A model of contractual disputes," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 494-504.
    7. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    8. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2005. "A Canonical Model for Interactive Unawareness," Bonn Econ Discussion Papers bgse23_2005, University of Bonn, Germany.
    9. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
    10. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    11. Burkhard C. Schipper & Aviad Heifetz & Martin Meier, 2007. "Unawareness, Beliefs and Games," Working Papers 73, University of California, Davis, Department of Economics.
    12. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    13. Zhao, Xiaojian, 2011. "Framing contingencies in contracts," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 31-40, January.
    14. 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.
    15. 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).
    16. Feinberg, Yossi, 2004. "Subjective Reasoning--Games with Unawareness," Research Papers 1875, Stanford University, Graduate School of Business.
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    Cited by:
    1. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.

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