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Counting combinatorial choice rules

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  • Echenique, Federico

Abstract

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 asymptotically 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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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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Find related papers by JEL classification:
  • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  1. Martine Quinzii & Carmen Bevia & JosÅ A. Silva, 2003. "Buying Several Indivisible Goods," Working Papers 9720, University of California, Davis, Department of Economics.
  2. 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.
  3. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  4. repec:cup:cbooks:9780521424585 is not listed on IDEAS
  5. Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, vol. 15(4), pages 559-562.
  6. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  7. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  8. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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Cited by:

  1. Federico Echenique, 2005. "A Solution to Matching with Preferences over Colleagues," Game Theory and Information 0506005, EconWPA.
  2. Utku Unver & Hideo Konishi, 2005. "Credible Group Stability in Multi-Partner Matching Problems," 2005 Meeting Papers 208, Society for Economic Dynamics.
  3. Ilya Segal, 2004. "The Communication Requirements of of Social Choice Rules and Supporting Budget Sets," Economics Working Papers 0039, Institute for Advanced Study, School of Social Science.
  4. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 341-378, September.
  5. Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena 629, Department of Economics, University of Siena.
  6. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.

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