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Bayesian games with unawareness and unawareness perfection

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  • Martin Meier
  • Burkhard Schipper

Abstract

Applying unawareness belief structures introduced in Heifetz et al. (Games Econ Behav 77:100–121, 2013a ), 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 apply Bayesian games with unawareness to investigate the robustness of equilibria to uncertainty about opponents’ awareness of actions. We show that a Nash equilibrium of a strategic game is robust to unawareness of actions if and only if it is not weakly dominated. Finally, we discuss the relationship between standard Bayesian games and Bayesian games with unawareness. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:56:y:2014:i:2:p:219-249
    DOI: 10.1007/s00199-013-0788-5
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    Citations

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    Cited by:

    1. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    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. Li, Sanxi & Peitz, Martin & Zhao, Xiaojian, 2016. "Information disclosure and consumer awareness," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 209-230.
    5. 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.
    6. John Quiggin, 2017. "Dynamic awareness and zero probability beliefs," Theory and Decision, Springer, vol. 83(3), pages 309-313, October.
    7. 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.
    8. Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    9. Antoine Dubus, 2020. "Asymmetric awareness and heterogeneous agents," Rationality and Society, , vol. 32(4), pages 461-484, November.
    10. 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.
    11. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    12. Galanis, Spyros, 2018. "Speculation under unawareness," Games and Economic Behavior, Elsevier, vol. 109(C), pages 598-615.
    13. Katarina Kostelić, 2023. "Implications of (un)awareness for decision-making in strategic interaction: another take on the Prisoner’s dilemma," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(2), pages 251-268, June.
    14. Bahel, Eric & Haller, Hans, 2013. "Cycles with undistinguished actions and extended Rock–Paper–Scissors games," Economics Letters, Elsevier, vol. 120(3), pages 588-591.
    15. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.
    16. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.

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    More about this item

    Keywords

    Unawareness; Awareness; Type-space; Incomplete information; Bayesian games; Equilibrium; Perfection ; Undominated equilibrium; Weak dominance; Admissibility ; Inattention; C70; C72; D80; D82;
    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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