IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/854.html
   My bibliography  Save this paper

A Game-Theoretic Approach to the Binary Stochastic Choice Problem

Author

Listed:
  • Itzhak Gilboa
  • Dov Monderer

Abstract

We provide an equivalence theorem for the binary stochastic choice problem, which may be thought of as an implicit characterization of binary choice probabilities which are consistent with a probability over linear orderings. In some cases this implicit characterization is very useful in derivation of explicit necessary conditions. In particular, we present a new set of conditions which generalizes both Cohen and Falmagne's and Fishburn's conditions.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Itzhak Gilboa & Dov Monderer, 1989. "A Game-Theoretic Approach to the Binary Stochastic Choice Problem," Discussion Papers 854, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:854
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/research/math/papers/854.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Itzhak Gilboa, 1989. "A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem," Discussion Papers 818, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    3. Gilboa, Itzhak & Monderer, Dov, 1991. "Quasi-values on Subspaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 353-363.
    4. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    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. Yohan Pelosse, 2024. "A Non-Cooperative Shapley Value Representation of Luce Contests Success Functions," Working Papers 2024-01, Swansea University, School of Management.
    2. Gilboa, Itzhak & Monderer, Dov, 1991. "Quasi-values on Subspaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 353-363.
    3. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.

    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. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    2. Daniele Caliari & Henrik Petri, 2024. "Irrational Random Utility Models," Papers 2403.10208, arXiv.org.
    3. Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 643-658, October.
    4. Dasgupta Indraneel & Pattanaik P. K, 2010. "Revealed Preference with Stochastic Demand Correspondence," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, August.
    5. Itzhak Gilboa, 1989. "A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem," Discussion Papers 818, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    7. Batley, Richard & Hess, Stephane, 2016. "Testing for regularity and stochastic transitivity using the structural parameter of nested logit," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 355-376.
    8. Richter, Marcel K. & Wong, Kam-Chau, 2016. "Likelihood relations and stochastic preferences," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 28-35.
    9. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    10. Jan Heufer, 2011. "Stochastic revealed preference and rationalizability," Theory and Decision, Springer, vol. 71(4), pages 575-592, October.
    11. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.
    12. McClellon, Morgan, 2016. "Confidence models of incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 30-34.
    13. Changkuk Im & John Rehbeck, 2021. "Non-rationalizable Individuals, Stochastic Rationalizability, and Sampling," Papers 2102.03436, arXiv.org, revised Oct 2021.
    14. Soren Blomquist & Anil Kumar & Che-Yuan Liang & Whitney K. Newey, 2022. "Nonlinear Budget Set Regressions for the Random Utility Model," Working Papers 2219, Federal Reserve Bank of Dallas.
    15. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    16. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    17. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2019. "Deliberately Stochastic," American Economic Review, American Economic Association, vol. 109(7), pages 2425-2445, July.
      • Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2012. "Deliberately Stochastic," PIER Working Paper Archive 17-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 May 2017.
    18. repec:zbw:rwirep:0070 is not listed on IDEAS
    19. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
    20. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    21. Steven T. Berry & Philip A. Haile, 2024. "Nonparametric Identification of Differentiated Products Demand Using Micro Data," Econometrica, Econometric Society, vol. 92(4), pages 1135-1162, July.

    More about this item

    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:nwu:cmsems:854. 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: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.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.