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

Author

Listed:
  • 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.

Suggested Citation

  • Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 723-749.
  • 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 listed on IDEAS

    as
    1. Francis Su, "undated". "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
    2. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 201-215.
    3. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    4. 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.
    5. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
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    Citations

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    Cited by:

    1. Edith Cohen & Michal Feldman & Amos Fiat & Haim Kaplan & Svetlana Olonetsky, 2010. "Envy-Free Makespan Approximation," Discussion Paper Series dp539, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
    3. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2014. "Least manipulable Envy-free rules in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 43-49.
    4. Azacis, Helmuts, 2008. "Double implementation in a market for indivisible goods with a price constraint," Games and Economic Behavior, Elsevier, vol. 62(1), pages 140-154, January.
    5. 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.
    6. Fragnelli, Vito & Marina, Maria Erminia, 2003. "A fair procedure in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 75-85, August.
    7. 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.
    8. Ning Sun & Zaifu Yang, 2009. "Strategy Proof And Privacy Preserving Fair Allocation Mechanism," The Japanese Economic Review, Japanese Economic Association, vol. 60(2), pages 143-151.
    9. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506 Elsevier.
    10. ANDERSSON, Tommy & EHLERS, Lars, 2013. "An algorithm for identifying agent-k-linked allocations in economies with indivisibilities," Cahiers de recherche 2013-12, Universite de Montreal, Departement de sciences economiques.
    11. 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.
    12. Tommy Andersson & Christer Andersson, 2009. "Solving House Allocation Problems with Risk-Averse Agents," Computational Economics, Springer;Society for Computational Economics, vol. 33(4), pages 389-401, May.
    13. 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.
    14. repec:eee:matsoc:v:89:y:2017:i:c:p:100-108 is not listed on IDEAS
    15. Clark Bowman & Jonathan Hodge & Ada Yu, 2014. "The potential of iterative voting to solve the separability problem in referendum elections," Theory and Decision, Springer, vol. 77(1), pages 111-124, June.
    16. Atila Abdulkadiroğlu & Tayfun Sönmez & M. Utku Ünver, 2004. "Room assignment-rent division: A market approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 515-538, June.
    17. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2012. "(Minimally) 'epsilon'-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche 2012-03, Universite de Montreal, Departement de sciences economiques.
    18. Ehtamo, Harri & Kettunen, Eero & Hamalainen, Raimo P., 2001. "Searching for joint gains in multi-party negotiations," European Journal of Operational Research, Elsevier, vol. 130(1), pages 54-69, April.
    19. Mu'alem, Ahuva, 2014. "Fair by design: Multidimensional envy-free mechanisms," Games and Economic Behavior, Elsevier, vol. 88(C), pages 29-46.
    20. repec:spr:grdene:v:11:y:2002:i:5:d:10.1023_a:1020485018300 is not listed on IDEAS
    21. Edith Cohen & Michal Feldman & Amos Fiat & Haim Kaplan & Svetlana Olonetsky, 2010. "Truth and Envy in Capacitated Allocation Games," Discussion Paper Series dp540, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    22. 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.
    23. Daniela Ambrosino & Vito Fragnelli & Maria Marina, 2006. "Resolving an Insurance Allocation Problem: A Procedural Approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 625-643, June.

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