IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/01-2013.html
   My bibliography  Save this paper

Every Choice Function is Backwards-Induction Rationalizable

Author

Listed:
  • 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.

Suggested Citation

  • Walter Bossert & Yves Sprumont, 2013. "Every Choice Function is Backwards-Induction Rationalizable," Cahiers de recherche 01-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:01-2013
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/01-2013-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    2. Ray, Indrajit & Zhou, Lin, 2001. "Game Theory via Revealed Preferences," Games and Economic Behavior, Elsevier, vol. 37(2), pages 415-424, November.
    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.
    4. Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, vol. 134(1), pages 548-556, May.
    5. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
    6. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    7. Adam Galambos, 2005. "Revealed Preference in Game Theory," 2005 Meeting Papers 776, Society for Economic Dynamics.
    8. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    10. Rehbeck, John, 2018. "Note on unique Nash equilibrium in continuous games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 216-225.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rehbeck, John, 2014. "Every choice correspondence is backwards-induction rationalizable," Games and Economic Behavior, Elsevier, vol. 88(C), pages 207-210.
    2. Li, Jiangtao & Tang, Rui, 2017. "Every random choice rule is backwards-induction rationalizable," Games and Economic Behavior, Elsevier, vol. 104(C), pages 563-567.
    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.
    4. Pierre-André Chiappori & Olivier Donni, 2005. "Learning From a Piece of Pie: The Empirical Content of Nash Bargaining," THEMA Working Papers 2006-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. 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.
    6. Freer, Mikhail & Martinelli, César, 2021. "A utility representation theorem for general revealed preference," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 68-76.
    7. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
    8. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    9. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    10. Lee, Byung Soo & Stewart, Colin, 2016. "Identification of payoffs in repeated games," Games and Economic Behavior, Elsevier, vol. 99(C), pages 82-88.
    11. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    12. Andrés Carvajal & Rahul Deb & James Fenske & John Quah, 2014. "A nonparametric analysis of multi-product oligopolies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 253-277, October.
    13. Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
    14. Yariv, Leeat & Jackson, Matthew O., 2018. "The Non-Existence of Representative Agents," CEPR Discussion Papers 13397, C.E.P.R. Discussion Papers.
    15. Momi, Takeshi, 2010. "Excess demand function around critical prices in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 293-302, May.
    16. Ghiglino, Christian & Tvede, Mich, 1997. "Multiplicity of Equilibria," Journal of Economic Theory, Elsevier, vol. 75(1), pages 1-15, July.
    17. Andrés Carvajal, 2003. "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," Borradores de Economia 229, Banco de la Republica de Colombia.
    18. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    19. Gerard Ballot & Antoine Mandel & Annick Vignes, 2015. "Agent-based modeling and economic theory: where do we stand?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 199-220, October.
    20. Chiappori, Pierre-Andre & Ekeland, Ivar & Browning, Martin, 2007. "Local disaggregation of negative demand and excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 764-770, August.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montec:01-2013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.