The computational complexity of rationalizing Pareto optimal choice behavior
We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.
|Date of creation:||Jun 2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +32-(0)16-32 67 25
Fax: +32-(0)16-32 67 96
Web page: http://www.econ.kuleuven.be/ew
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007.
"The Collective Model of Household Consumption: A nonparametric characterization,"
ULB Institutional Repository
2013/98559, ULB -- Universite Libre de Bruxelles.
- Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, 03.
- Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2004. "The Collective Model of Household Consumption : A Nonparametric Characterization," Discussion Paper 2004-76, Tilburg University, Center for Economic Research.
- Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2007. "The collective model of household consumption : A nonparametric characterization," Other publications TiSEM 0a104373-4fb6-4ef2-9d2b-2, Tilburg University, School of Economics and Management.
- Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
- Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
- Rees, Ray, 1988. "Taxation and the Household," Munich Reprints in Economics 3411, University of Munich, Department of Economics.
- Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
- Talla Nobibon, Fabrice & Spieksma, Frits C.R., 2010. "On the complexity of testing the Collective Axiom of Revealed Preference," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 123-136, September.
- Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, vol. 134(1), pages 548-556, May.
- Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
- Chiappori, Pierre-Andre, 1992.
"Collective Labor Supply and Welfare,"
Journal of Political Economy,
University of Chicago Press, vol. 100(3), pages 437-67, June.
- repec:ner:tilbur:urn:nbn:nl:ui:12-194157 is not listed on IDEAS
- Bossert, Walter & Suzumura, Kotaro, 2010.
"Consistency, Choice, and Rationality,"
Harvard University Press, number 9780674052994.
- Echenique, Federico & Ivanov, Lozan, 2011.
"Implications of Pareto efficiency for two-agent (household) choice,"
Journal of Mathematical Economics,
Elsevier, vol. 47(2), pages 129-136, March.
- Echenique, Federico & Ivanov, Lozan, . "Implications of Pareto Efficiency for two-agent (household) choice," Working Papers 1308, California Institute of Technology, Division of the Humanities and Social Sciences.
- Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002.
"Rationalizing Choice Functions By Multiple Rationales,"
Econometric Society, vol. 70(6), pages 2481-2488, November.
- Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Discussion Paper Series dp278, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Gil Kalai & Ariel Rubenstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Economics Working Papers 0010, Institute for Advanced Study, School of Social Science.
- Chiappori, Pierre-Andre, 1988. "Nash-Bargained Households Decisions: A Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 791-96, November.
- Apps, Patricia F. & Rees, Ray, 1988. "Taxation and the household," Journal of Public Economics, Elsevier, vol. 35(3), pages 355-369, April.
- Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
When requesting a correction, please mention this item's handle: RePEc:ete:ceswps:ces11.13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Karla Vander Weyden)
If references are entirely missing, you can add them using this form.