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Games with Unawareness

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  • Feinberg, Yossi

    (Stanford University)

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.

Suggested Citation

  • Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
  • Handle: RePEc:ecl:stabus:2122
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    File URL: https://gsbapps.stanford.edu/researchpapers/library/RP2122.pdf
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    References listed on IDEAS

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    1. Gossner, O. & Tsakas, E., 2010. "A reasoning approach to introspection and unawareness," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 131-155, February.
    3. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    4. Zhao, Xiaojian, 2011. "Framing contingencies in contracts," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 31-40, January.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2007. "Unawareness, Beliefs and Games," Bonn Econ Discussion Papers 6/2007, University of Bonn, Bonn Graduate School of Economics (BGSE).
    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. Xiaojian Zhao, 2008. "Moral Hazard With Unawareness," Rationality and Society, , vol. 20(4), pages 471-496, November.
    8. Oliver Board, 2008. "Object-Based Unawareness: Theory and Applications," Working Paper 378, Department of Economics, University of Pittsburgh, revised Mar 2009.
    9. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    10. 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.
    11. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    12. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    13. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    14. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    15. Feinberg, Yossi, 2004. "Subjective Reasoning--Games with Unawareness," Research Papers 1875, Stanford University, Graduate School of Business.
    16. Ernst-Ludwig Von Thadden & Xiaojian Zhao, 2012. "Incentives for Unaware Agents," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1151-1174.
    17. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
    18. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    19. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
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    Citations

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    Cited by:

    1. Liu, Zhen, 2016. "Games with incomplete information when players are partially aware of others’ signals," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 58-70.
    2. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    3. Yasuo Sasaki, 2016. "An Equivalence Result on the Reduction of Games with Unawareness," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-27, September.
    4. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    5. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    6. Burkhard Schipper, 2011. "Preference-Dependent Unawareness," Working Papers 269, University of California, Davis, Department of Economics.
    7. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    8. Yasuo Sasaki, 2017. "Generalized Nash equilibrium with stable belief hierarchies in static games with unawareness," Annals of Operations Research, Springer, vol. 256(2), pages 271-284, September.
    9. Galanis, Spyros, 2018. "Speculation under unawareness," Games and Economic Behavior, Elsevier, vol. 109(C), pages 598-615.
    10. Araujo, Felipe A. & Piermont, Evan, 2023. "Unawareness and risk taking: The role of context," Journal of Economic Behavior & Organization, Elsevier, vol. 208(C), pages 61-79.
    11. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    12. Liu, Chanjuan & Zhu, Enqiang, 2017. "Computational ability in games: Individual difference and dynamics," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 313-320.
    13. 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.
    14. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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