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On The Complexity of Rationalizing Behavior

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  • Jose Apesteguia
  • Miguel A Ballester

Abstract

We study the complexity of rationalizing choice behavior. We do so by analyzing two polar cases, and a number of intermediate ones. In our most structured case, that is where choice behavior is defined in universal choice domains and satisfies the "weak axiom of revealed preference," Finding the complete preorder rationalizing choice behavior is a simple matter. In the polar case, where no restriction whatsoever is imposed, either on choice behavior or on choice domain, Finding the complete preorders that rationalize behavior turns out to be intractable. We show that the task of finding the rationalizing complete preorders is equivalent to a graph problem. This allows the search for existing algorithms in the graph theory literature, for the rationalization of choice.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 320.

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Date of creation: Aug 2007
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Handle: RePEc:bge:wpaper:320

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Keywords: Rationalization; Computational complexity; NP-complete; Arbitrary choice domains.;

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  1. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Discussion Paper Series dp278, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  3. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2003. "Fact-Free Learning," PIER Working Paper Archive 05-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2004.
  4. Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, vol. 134(1), pages 548-556, May.
  5. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," Discussion Paper Series dp320, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  6. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  7. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
  8. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," NajEcon Working Paper Reviews 666156000000000082, www.najecon.org.
  9. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
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