Testing Consumer Rationality Using Perfect Graphs and Oriented Discs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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© Springer-Verlag Berlin Heidelberg 2015

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Department of Mathematics and Statistics, and School of Computer ScienceMcGill UniversityMontrealCanada

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