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Counting combinatorial choice rules

  • Echenique, Federico

I count the number of combinatorial choice rules that satisfy certain properties: Kelso-Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymtotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents---which has positive implications for the Gale-Shapley algorithm of matching theory.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4JW7WWP-2/2/462f48483ea17f25dcec1e56434dc03d
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 58 (2007)
Issue (Month): 2 (February)
Pages: 231-245

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Handle: RePEc:eee:gamebe:v:58:y:2007:i:2:p:231-245
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Carmen Beviá Baeza & José Angel Silva Reus, 1997. "Buying several indivisible goods," Working Papers. Serie AD 1997-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  3. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  4. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
  5. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  6. repec:cup:cbooks:9780521424585 is not listed on IDEAS
  7. Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, vol. 15(4), pages 559-562.
  8. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
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