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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)

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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Bibliographic Info

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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References

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  1. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  2. Brams, S.J. & Kilgour, D.M., 1999. "Competitive Fair Division," Working Papers 99-05, C.V. Starr Center for Applied Economics, New York University.
  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.
  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.
  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.
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Cited by:
  1. Helmuts Azacis, 2004. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," UFAE and IAE Working Papers 623.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Atila Abdulkadiroglu & Tayfun Sonmez & M. Utku Unver, 2002. "Room Assignment-Rent Division: A Market Approach," Game Theory and Information 0202003, EconWPA, revised 26 Sep 2002.
  3. Edith Cohen & Michal Feldman & Amos Fiat & Haim Kaplan & Svetlana Olonetsky, 2010. "Envy-Free Makespan Approximation," Discussion Paper Series dp539, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. 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.
  5. Tommy Andersson & Christer Andersson, 2009. "Solving House Allocation Problems with Risk-Averse Agents," Computational Economics, Society for Computational Economics, vol. 33(4), pages 389-401, May.
  6. Vito Fragnelli & Maria Erminia Marina, 2009. "Strategic Manipulations and Collusions in Knaster Procedure," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 3(2), pages 143-153, July.
  7. Edith Cohen & Michal Feldman & Amos Fiat & Haim Kaplan & Svetlana Olonetsky, 2010. "Truth and Envy in Capacitated Allocation Games," Discussion Paper Series dp540, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. Fragnelli, Vito & Marina, Maria Erminia, 2003. "A fair procedure in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 75-85, August.
  9. Simmons, Forest W. & Su, Francis Edward, 2003. "Consensus-halving via theorems of Borsuk-Ulam and Tucker," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 15-25, February.
  10. Richard Hule & Matthias Sutter, 2003. "Can the Stability and Growth Pact in EMU Cause Budget Deficit Cycles?," Empirica, Springer, vol. 30(1), pages 25-38, March.
  11. Andersson, T. & Svensson, L.-G. & Yang, Z., 2010. "Constrainedly fair job assignments under minimum wages," Games and Economic Behavior, Elsevier, vol. 68(2), pages 428-442, March.
  12. Andersson , Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2012. "e-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Working Papers 2012:8, Lund University, Department of Economics.

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