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Conditional dominance in games with unawareness

Author

Listed:
  • Martin Meier
  • Burkhard C. Schipper

    (Department of Economics, University of California Davis)

Abstract

Heifetz, Meier and Schipper (2013) introduced generalized extensive-form games that allow for asymmetric unawareness. Here, we study the normal form of a generalized extensive-form game. The generalized normal-form game associated to a generalized extensive-form game with unawareness may consist of a collection of normal-form games. We use it to characterize extensive-form rationalizability (resp. prudent rationalizability) in generalized extensive-form games by iterative conditional strict (resp. weak) dominance in the associated generalized normal-form. We also show that the analogue to iterated admissibility for generalized normal-form games is not independent of the extensive-form structure. This is because under unawareness, a player's information set not only determines which nodes he considers possible but also of which game tree(s) he is aware of.

Suggested Citation

  • Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:351
    as

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    File URL: https://repec.dss.ucdavis.edu/files/1xNTcwdu2yysGCxYcPnT8Ktp/condom20230426.pdf
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    References listed on IDEAS

    as
    1. Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
    2. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    4. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    5. Sarah Auster & Nicola Pavoni, 2021. "Optimal Delegation and Information Transmission under Limited Awareness," ECONtribute Discussion Papers Series 059, University of Bonn and University of Cologne, Germany.
    6. Filiz-Ozbay, Emel, 2012. "Incorporating unawareness into contract theory," Games and Economic Behavior, Elsevier, vol. 76(1), pages 181-194.
    7. 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.
    8. Ernst-Ludwig Von Thadden & Xiaojian Zhao, 2012. "Incentives for Unaware Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1151-1174.
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    10. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    11. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    12. 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.
    13. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.
    14. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
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    22. 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.
    23. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
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    Cited by:

    1. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    Awareness; unknown unknowns; extensive-form rationalizability; prudent rationalizability; iterated admissibility; iterated conditional dominance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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