IDEAS home Printed from https://ideas.repec.org/p/osk/wpaper/1517r.html
   My bibliography  Save this paper

Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test

Author

Listed:
  • Kohei Shiozawa

    (Graduate School of Economics, Osaka University)

Abstract

This paper presents some substantial relationships between revealed preference tests for a data set and the shortest path problem in a network (a directed graph with weighted edges), using a simple and straightforward graph theoretic argument. We clarify the interpretation of revealed preference tests, refine Afriat inequalities, and give a unified perspective of several forms of rationalizability tests and the classical utility representation problem of preferences. Furthermore, we provide an additional graph theoretic structure, which we call the shortest path problem with weight adjustment. This is a common structure for several rationalizability tests. The proposed structure leads to effcient algorithms for checking rationalizability conditions, and for computing a solution to the Afriat inequalities if the data are rationalizable in several settings.

Suggested Citation

  • Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev., Osaka University, Graduate School of Economics, revised Jul 2015.
    • Handle: RePEc:osk:wpaper:1517r
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
    3. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    4. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    5. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    6. Satoru Fujishige & Zaifu Yang, 2012. "On Revealed Preference and Indivisibilities," Discussion Papers 12/02, Department of Economics, University of York.
    7. Bram De Rock & Bart Smeulders & Laurens Cherchye & Frits Spieksma, 2013. "Goodness of fit measures for revealed preference tests: Complexity results and algorithms," ULB Institutional Repository 2013/162939, ULB -- Universite Libre de Bruxelles.
    8. Bart Smeulders & Laurens Cherchye & Bram De Rock & Frits C. R. Spieksma, 2013. "The Money Pump as a Measure of Revealed Preference Violations: A Comment," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1248-1258.
    9. Kolesnikov, Alexander V. & Kudryavtseva, Olga V. & Nagapetyan, Tigran, 2013. "Remarks on Afriat’s theorem and the Monge–Kantorovich problem," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 501-505.
    10. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    11. Matthew Polisson & John K.-H. Quah, 2013. "Revealed Preference in a Discrete Consumption Space," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 28-34, February.
    12. Donald J. Brown & Caterina Calsamiglia, 2008. "The Nonparametric Approach to Applied Welfare Analysis," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 41-46, Springer.
    13. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    14. repec:dau:papers:123456789/11953 is not listed on IDEAS
    15. Kohei Shiozawa, 2015. "Note on the goodness-of-fit measure for GARP; NP-hardness of minimum cost index," Discussion Papers in Economics and Business 15-18, Osaka University, Graduate School of Economics.
    16. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    17. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
    18. repec:dau:papers:123456789/4099 is not listed on IDEAS
    19. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    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. Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.

    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. Shiozawa, Kohei, 2016. "Revealed preference test and shortest path problem; graph theoretic structure of the rationalizability test," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 38-48.
    2. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev.2, Osaka University, Graduate School of Economics, revised Aug 2016.
    3. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    4. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    5. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    6. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    7. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    8. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    9. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    10. Dziewulski, Paweł & Lanier, Joshua & Quah, John K.-H., 2024. "Revealed preference and revealed preference cycles: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    11. Thomas Demuynck & John Rehbeck, 2023. "Computing revealed preference goodness-of-fit measures with integer programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1175-1195, November.
    12. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    13. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    14. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    15. Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.
    16. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17, Osaka University, Graduate School of Economics.
    17. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.
    18. Ivar Ekeland & Alfred Galichon, 2013. "The housing problem and revealed preference theory: duality and an application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 425-441, November.
    19. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    20. Roy Allen & Paweł Dziewulski & John Rehbeck, 2024. "Revealed statistical consumer theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 823-847, May.
    21. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.

    More about this item

    Keywords

    Revealed preference; Afriat inequalities; shortest path problem;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    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:osk:wpaper:1517r. 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: The Economic Society of Osaka University (email available below). General contact details of provider: https://edirc.repec.org/data/feosujp.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.