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Rationalizable self-confirming equilibrium in static games with unawareness

Author

Listed:
  • Norimasa Kobayashi

    (Tokyo Institute of Technology)

  • Yasuo Sasaki

    (Gakushuin University)

Abstract

This paper discusses rationalizable self-confirming equilibrium (RSCE) in static games with unawareness that captures steady states of such games. We begin by defining the equilibrium concept in terms of its epistemic conditions. k-RSCE is a situation in which agents make rational choices and have correct beliefs about one another’s choices, and moreover these can be mutual belief to the k-th order. We then present an alternative definition that dispenses with these epistemic conditions and allows us to obtain equilibria through iterative eliminations of certain action profiles. In standard static games, k-RSCE reduces to Nash equilibrium, but not under unawareness. We examine the equilibrium concept’s properties and clarify its relationships with other equilibrium concepts for games with unawareness.

Suggested Citation

  • Norimasa Kobayashi & Yasuo Sasaki, 2024. "Rationalizable self-confirming equilibrium in static games with unawareness," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 765-790, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00907-1
    DOI: 10.1007/s00182-024-00907-1
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    References listed on IDEAS

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    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    2. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    3. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.
    4. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    5. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    6. 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.
    7. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    8. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    9. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    10. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    11. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    12. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    13. ,, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
    14. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    15. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    16. 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.
    17. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    18. 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.
    19. 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.
    20. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    21. 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.
    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.
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