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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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Martine Quinzii & Carmen Bevia & JosÃ… A. Silva, 2003. "Buying Several Indivisible Goods," Working Papers, University of California, Davis, Department of Economics 9720, University of California, Davis, Department of Economics.
  2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, 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, Econometric Society, vol. 50(6), pages 1483-1504, November.
  4. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(2), pages 324-363, April.
  5. Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, Springer, vol. 15(4), pages 559-562.
  6. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
  7. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, 9.
  8. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 66-95, May.
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Cited by:
  1. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, Elsevier, vol. 59(1), pages 46-71, April.
  2. Utku Unver & Hideo Konishi, 2005. "Credible Group Stability in Multi-Partner Matching Problems," 2005 Meeting Papers, Society for Economic Dynamics 208, Society for Economic Dynamics.
  3. Ilya Segal, 2004. "The Communication Requirements of of Social Choice Rules and Supporting Budget Sets," Economics Working Papers, Institute for Advanced Study, School of Social Science 0039, Institute for Advanced Study, School of Social Science.
  4. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics, Boston College Department of Economics 805, Boston College Department of Economics.
  5. Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena, Department of Economics, University of Siena 629, Department of Economics, University of Siena.
  6. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 341-378, September.

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