IDEAS home Printed from https://ideas.repec.org/p/aut/wpaper/2024-03.html
   My bibliography  Save this paper

Cycle conditions for "Luce rationality"

Author

Listed:
  • Jose A. Rodrigues-Neto

    (Research School of Economics, Australian National University)

  • Matthew Ryan

    (Department of Economics and Finance, Auckland University of Technology)

  • James Taylor

    (Research School of Economics, Australian National University)

Abstract

We extend and refine conditions for "Luce rationality" (i.e., the existence of a Luce - or logit - model) in the context of stochastic choice. When choice probabilities satisfy positivity, we show that the cyclical independence (CI) condition of Ahumada and Ulku (2018) and Echenique and Saito (2019) is necessary and sufficient for Luce rationality, even if choice is only observed for a restricted set of menus. We then adapt results from the cycles approach (Rodrigues-Neto, 2009) to the common prior problem (Harsanyi, 1967-1968) to refine the CI condition, by reducing the number of cycle equations that need to be checked. A general algorithm is provided to identify a minimal sufficient set of equations (depending on the collection of menus for which choice is observed). Three cases are discussed in detail: (i) when choice is only observed from binary menus, (ii) when all menus contain a common default; and (iii) when all menus contain an element from a common binary default set. Investigation of case (i) leads to a refinement of the famous product rule.

Suggested Citation

  • Jose A. Rodrigues-Neto & Matthew Ryan & James Taylor, 2024. "Cycle conditions for "Luce rationality"," Working Papers 2024-03, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:2024-03
    as

    Download full text from publisher

    File URL: https://www.aut.ac.nz/__data/assets/pdf_file/0009/884178/working-paper-2024_03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    Full references (including those not matched with items on IDEAS)

    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. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    2. Collevecchio, Andrea & LiCalzi, Marco, 2012. "The probability of nontrivial common knowledge," Games and Economic Behavior, Elsevier, vol. 76(2), pages 556-570.
    3. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    4. Halpern, Joseph Y. & Kets, Willemien, 2015. "Ambiguous language and common priors," Games and Economic Behavior, Elsevier, vol. 90(C), pages 171-180.
    5. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    6. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    7. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    8. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    9. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    10. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    11. Christian W. Bach & Andrés Perea, 2023. "Structure‐preserving transformations of epistemic models," Economic Inquiry, Western Economic Association International, vol. 61(3), pages 693-719, July.
    12. Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194, March.
    13. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

    More about this item

    Keywords

    :;

    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:aut:wpaper:2024-03. 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: Gail Pacheco (email available below). General contact details of provider: https://edirc.repec.org/data/fbautnz.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.