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

  • 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)

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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  1. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  2. 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.
  3. 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.
  4. Brams, S.J. & Kilgour, D.M., 1999. "Competitive Fair Division," Working Papers 99-05, C.V. Starr Center for Applied Economics, New York University.
  5. 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.
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