Counting Combinatorial Choice Rules
AbstractI 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 InfoPaper provided by EconWPA in its series Game Theory and Information with number 0404004.
Length: 18 pages
Date of creation: 30 Apr 2004
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Substitutability; Choice rules; Matching markets; Gale-Shapley Algorithm;
Other versions of this item:
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
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- Martine Quinzii & Carmen Bevia & JosÅ A. Silva, 2003.
"Buying Several Indivisible Goods,"
9720, University of California, Davis, Department of Economics.
- 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).
- Carmen Bevia & Martine Quinzii & JosŽ A. Silva, . "Buying Several Indivisible Goods," Department of Economics 97-20, California Davis - Department of Economics.
- Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
- Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
- Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, October.
- 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.
- Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, vol. 15(4), pages 559-562.
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
- Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena 629, Department of Economics, University of Siena.
- Utku Unver & Hideo Konishi, 2005.
"Credible Group Stability in Multi-Partner Matching Problems,"
2005 Meeting Papers
208, Society for Economic Dynamics.
- Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
- Hideo Konishi & Utku Unver, 2004. "Credible Group Stability in Multi-Partner Matching Problems," Econometric Society 2004 North American Summer Meetings 32, Econometric Society.
- 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.
- 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.
- Echenique, Federico & Yenmez, Mehmet B., 2005.
"A Solution to Matching with Preferences over Colleagues,"
1226, California Institute of Technology, Division of the Humanities and Social Sciences.
- Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
- Federico Echenique, 2005. "A Solution to Matching with Preferences over Colleagues," Game Theory and Information 0506005, EconWPA.
- Federico Echenique & Mehmet B. Yenmez, 2005. "A Solution to Matching with Preferences over Colleagues," Working Papers 2005.120, Fondazione Eni Enrico Mattei.
- 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.
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