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Counting Combinatorial Choice Rules

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Author Info
Federico Echenique (California Institute of Technology)

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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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File URL: http://129.3.20.41/eps/game/papers/0404/0404004.pdf
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Publisher Info
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
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Handle: RePEc:wpa:wuwpga:0404004

Note: Type of Document - pdf; pages: 18
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Web page: http://129.3.20.41

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Related research
Keywords: Substitutability; Choice rules; Matching markets; Gale-Shapley Algorithm;

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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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
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This page was last updated on 2009-11-5.

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