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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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  1. 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.
  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.
  3. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  4. 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.
  5. 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.
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Cited by:
  1. 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.
  2. 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.
  3. Fragnelli, Vito & Marina, Maria Erminia, 2003. "A fair procedure in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 75-85, August.
  4. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. 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.
  6. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Cahiers de recherche 18-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. 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.
  8. 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.
  9. Tommy Andersson & Lars Ehlers & Lars-Gunnar Svensson, 2012. "(Minimally) ?-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche 04-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. 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.
  11. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2012. "Least Manipulable Envy-free Rules in Economies with Indivisibilities," Working Papers 2012:8, Lund University, Department of Economics, revised 30 Sep 2013.
  12. 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.
  13. 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.
  14. 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.

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