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. Copyright Springer-Verlag Berlin Heidelberg 2014
Volume (Year): 42 (2014)
Issue (Month): 3 (March)
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- 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.
- Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
- Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
- 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 Rubenstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Economics Working Papers 0010, Institute for Advanced Study, School of Social Science.
- 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.
- Apps, Patricia F. & Rees, Ray, 1988. "Taxation and the household," Journal of Public Economics, Elsevier, vol. 35(3), pages 355-369, April.
- Chiappori, Pierre-Andre, 1992.
"Collective Labor Supply and Welfare,"
Journal of Political Economy,
University of Chicago Press, vol. 100(3), pages 437-67, June.
- Rees, Ray, 1988. "Taxation and the Household," Munich Reprints in Economics 3411, University of Munich, Department of Economics.
- 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.
- Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2004.
"The Collective Model of Household Consumption : A Nonparametric Characterization,"
2004-76, Tilburg University, Center for Economic Research.
- 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., 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.
- 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.
- Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
- Bossert, Walter & Suzumura, Kotaro, 2009.
"Consistency, Choice and Rationality,"
PIE/CIS Discussion Paper
428, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
- Echenique, Federico & Ivanov, Lozan, .
"Implications of Pareto Efficiency for two-agent (household) choice,"
1308, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
- 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.
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