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Bidding for envy-freeness: A procedural approach to n-player fair-division problems

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Author Info
Claus-Jochen Haake () (Institute of Mathematical Economics, University of Bielefeld, P.O. Box 100131, 33501 Bielefeld, Germany)
Matthias G. Raith () (Department of Economics, University of Magdeburg, P.O. Box 4120, 39016 Magdeburg, Germany)
Francis Edward Su () (Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA)

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Abstract

We develop a procedure for implementing an efficient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments, assuming that players have quasi-linear utility functions. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 19 (2002)
Issue (Month): 4 ()
Pages: 723-749
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Handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:723-749

Note: Received: 6 March 2000/Accepted: 21 May 2001
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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. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges. [Downloadable!]
  2. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April. [Downloadable!] (restricted)
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  3. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer, vol. 17(2), pages 201-215. [Downloadable!] (restricted)
  4. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-54, July. [Downloadable!] (restricted)
  5. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-39, July. [Downloadable!] (restricted)
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(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. Azacis, Helmuts, 2005. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," Cardiff Economics Working Papers E2005/10, Cardiff University, Cardiff Business School, Economics Section. [Downloadable!]
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  2. Daniela Ambrosino & Vito Fragnelli & Maria Marina, 2006. "Resolving an Insurance Allocation Problem: A Procedural Approach," Social Choice and Welfare, Springer, vol. 26(3), pages 625-643, June. [Downloadable!] (restricted)
  3. Brams, S. J. & Eldelman, P. H. & Fishburn, P. C., 2000. "Paradoxes of Fair Division," Working Papers 00-13, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  4. Atila Abdulkadiroglu & Tayfun Sonmez & M. Utku Unver, 2002. "Room assignment-rent division: A market approach," Discussion Papers 0102-11, Columbia University, Department of Economics. [Downloadable!]
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