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Every Choice Function Is Backwards‐Induction Rationalizable

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  • Walter Bossert
  • Yves Sprumont

Abstract

A choice function is backwards-induction rationalizable if there exists a finite perfect-information extensive-form game such that, for each subset of alternatives, the backwards-induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards-induction rationalizable.
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Suggested Citation

  • Walter Bossert & Yves Sprumont, 2013. "Every Choice Function Is Backwards‐Induction Rationalizable," Econometrica, Econometric Society, vol. 81(6), pages 2521-2534, November.
    • Handle: RePEc:ecm:emetrp:v:81:y:2013:i:6:p:2521-2534
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    References listed on IDEAS

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    1. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
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    3. Ray, Indrajit & Snyder, Susan, 2013. "Observable implications of Nash and subgame-perfect behavior in extensive games," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 471-477.
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    Cited by:

    1. Li, Jiangtao & Tang, Rui, 2017. "Every random choice rule is backwards-induction rationalizable," Games and Economic Behavior, Elsevier, vol. 104(C), pages 563-567.
    2. Ray, Indrajit & Snyder, Susan, 2013. "Observable implications of Nash and subgame-perfect behavior in extensive games," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 471-477.
    3. Nishimura, Hiroki, 2021. "Revealed preferences of individual players in sequential games," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    4. Ray, Indrajit & Snyder, Susan, 2013. "Observable implications of Nash and subgame-perfect behavior in extensive games," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 471-477.
    5. Yan Zhao & Yuan Ni, 2022. "The Pricing Strategy of Digital Content Resources Based on a Stackelberg Game," Sustainability, MDPI, vol. 14(24), pages 1-16, December.
    6. Rehbeck, John, 2014. "Every choice correspondence is backwards-induction rationalizable," Games and Economic Behavior, Elsevier, vol. 88(C), pages 207-210.
    7. Federico Echenique & Gerelt Tserenjigmid, 2023. "Revealed preferences for dynamically inconsistent models," Papers 2305.14125, arXiv.org, revised Jul 2023.
    8. Lee, Byung Soo & Stewart, Colin, 2016. "Identification of payoffs in repeated games," Games and Economic Behavior, Elsevier, vol. 99(C), pages 82-88.
    9. Carvajal, Andrés, 2024. "Recent advances on testability in economic equilibrium models," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    10. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    11. Christopher P. Chambers & Yusufcan Masatlioglu & Christopher Turansick, 2025. "Revealed Social Networks," Papers 2501.02609, arXiv.org, revised Jun 2025.
    12. Rehbeck, John, 2018. "Note on unique Nash equilibrium in continuous games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 216-225.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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