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Counting Combinatorial Choice Rules

  • Federico Echenique

    (California Institute of Technology)

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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File URL: http://128.118.178.162/eps/game/papers/0404/0404004.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0404004.

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Length: 18 pages
Date of creation: 30 Apr 2004
Date of revision:
Handle: RePEc:wpa:wuwpga:0404004
Note: Type of Document - pdf; pages: 18
Contact details of provider: Web page: http://128.118.178.162

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  1. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  2. Carmen Bevia & Martine Quinzii & JosŽ A. Silva, . "Buying Several Indivisible Goods," Department of Economics 97-20, California Davis - Department of Economics.
  3. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  4. Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, vol. 15(4), pages 559-562.
  5. 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.
  6. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  7. repec:cup:cbooks:9780521424585 is not listed on IDEAS
  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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