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International Conference on Web and Internet Economics

WINE 2015: Web and Internet Economics pp 187–200Cite as

Testing Consumer Rationality Using Perfect Graphs and Oriented Discs

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9470))

Abstract

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set. We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove this using a reduction from planar 3-sat that is based upon oriented-disc drawings.

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Notes

  1. 1.

    When ties are possible, this formulation is called the strong axiom of revealed preference; see Houthakker [17]. We refer the reader to the survey by Varian [29] for details concerning the assorted axioms of revealed preference.

  2. 2.

    By the (Weak) Perfect Graph Theorem [22], the complements of these classes of graphs are also perfect.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Montreal, Canada

    Shant Boodaghians

  2. Department of Mathematics and Statistics, and School of Computer Science, McGill University, Montreal, Canada

    Adrian Vetta

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  1. Shant Boodaghians
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  2. Adrian Vetta
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Correspondence to Shant Boodaghians .

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Editors and Affiliations

  1. Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

  2. CWI and VU Amsterdam, Amsterdam, The Netherlands

    Guido Schäfer

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Boodaghians, S., Vetta, A. (2015). Testing Consumer Rationality Using Perfect Graphs and Oriented Discs. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_14

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  • DOI: https://doi.org/10.1007/978-3-662-48995-6_14

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