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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
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    References listed on IDEAS

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    1. 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.
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    7. 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.
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    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.

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    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

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