The computational complexity of rationalizing boundedly rational choice behavior
We determine the computational complexity of various choice models that use multiple rationales to explain observed choice behavior. First, we demonstrate that the notion of rationalizability by K rationales, introduced by Kalai et al. (2002), is NP-complete for K greater than or equal to two. Then, we show that the question of sequential rationalizability by K rationales, introduced by Manzini and Mariotti (2007), is NP-complete for K greater than or equal to three. Finally, we focus on the computational complexity of two models that refine this model of sequential choice behavior. We establish that the model of choice by game trees, from Xu and Zhou (2007), is NP-complete while the status-quo bias model, from Masatlioglu and Ok (2005), can be verified in polynomial time.
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- Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
- Jose Apesteguia & Miguel�Angel Ballester, 2012.
"Choice By Sequential Procedures,"
615, Barcelona Graduate School of Economics.
- Jose Apesteguia & Miguel A. Ballester, 2012. "Choice by sequential procedures," Economics Working Papers 1309, Department of Economics and Business, Universitat Pompeu Fabra.
- Jose Apesteguia & Miguel Ballester, 2009. "Choice by Sequential Procedures," NajEcon Working Paper Reviews 814577000000000404, www.najecon.org.
- Eike B. Kroll & Bodo Vogt, 2008. "The Relevance of Irrelevant Alternatives: An experimental investigation of risky choices," FEMM Working Papers 08028, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
- Gilboa, Itzhak & Zemel, Eitan, 1989.
"Nash and correlated equilibria: Some complexity considerations,"
Games and Economic Behavior,
Elsevier, vol. 1(1), pages 80-93, March.
- Itzhak Gilboa & Eitan Zemel, 1988. "Nash and Correlated Equilibria: Some Complexity Considerations," Discussion Papers 777, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Samuelson, William & Zeckhauser, Richard, 1988. " Status Quo Bias in Decision Making," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 7-59, March.
- Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-65, March.
- Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
- Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
- Indrajit Ray & Lin Zhou, .
"Game Theory Via Revealed Preferences,"
00/15, Department of Economics, University of York.
- 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 Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, 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.
- Houy Nicolas, 2007. "Rationality and Order-Dependent Sequential Rationality," Theory and Decision, Springer, vol. 62(2), pages 119-134, March.
- Ariel Procaccia & Jeffrey Rosenschein & Aviv Zohar, 2008. "On the complexity of achieving proportional representation," Social Choice and Welfare, Springer, vol. 30(3), pages 353-362, April.
- Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer, vol. 20(3), pages 523-528, 06.
- Ehlers, Lars & Sprumont, Yves, 2008. "Weakened WARP and top-cycle choice rules," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 87-94, January.
- Richard Baron & Jacques Durieu & Hans Haller & Philippe Solal, 2004. "Finding a Nash equilibrium in spatial games is an NP-complete problem," Economic Theory, Springer, vol. 23(2), pages 445-454, January.
- Shanfeng Zhu & Xiaotie Deng & Maocheng Cai & Qizhi Fang, 2002. "On computational complexity of membership test in flow games and linear production games," International Journal of Game Theory, Springer, vol. 31(1), pages 39-45.
- Loomes, Graham & Starmer, Chris & Sugden, Robert, 1991. "Observing Violations of Transitivity by Experimental Methods," Econometrica, Econometric Society, vol. 59(2), pages 425-39, March.
- García-Sanz, María D. & Alcantud, José Carlos R., 2010. "Rational choice by two sequential criteria," MPRA Paper 21487, University Library of Munich, Germany.
- Francis Chu & Joseph Halpern, 2001.
"On the NP-completeness of finding an optimal strategy in games with common payoffs,"
International Journal of Game Theory,
Springer, vol. 30(1), pages 99-106.
- Francis C. Chu & Joseph Y. Halpern, 2000. "On the NP-Completeness of Finding an Optimal Strategy in Games with Common Payoffs," Game Theory and Information 0004011, EconWPA.
- Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, vol. 134(1), pages 548-556, May.
- Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
- Richard Baron & Jacques Durieu & Hans Haller & Philippe Solal & Savani Rahul, 2008. "Good neighbors are hard to find: computational complexity of network formation," Post-Print hal-00268851, HAL.
- Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, vol. 121(1), pages 1-29, March.
- Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
- Seidl, C. & Traub, S., 1996. "Rational Choice and the Relevance of Irrelevant Alternatives," Discussion Paper 1996-91, Tilburg University, Center for Economic Research.
- Richard Baron & Jacques Durieu & Hans Haller & Rahul Savani & Philippe Solal, 2008. "Good neighbors are hard to find: computational complexity of network formation," Review of Economic Design, Springer, vol. 12(1), pages 1-19, April.
- Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
- Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
- Felix Brandt & Felix Fischer & Paul Harrenstein & Maximilian Mair, 2010. "A computational analysis of the tournament equilibrium set," Social Choice and Welfare, Springer, vol. 34(4), pages 597-609, April.
- Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
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