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Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair Division Problems

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  • Claus-Jochen Haake

    (University of Bielefeld)

  • Matthias G. Raith

    (University of Bielefeld)

  • Francis Su

    (Harvey Mudd College)

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

Paper provided by Claremont Colleges in its series Claremont Colleges Working Papers with number 2000-47.

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Date of creation: 2000
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Handle: RePEc:clm:clmeco:2000-47

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References

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  1. 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.
  2. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  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. 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. 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.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  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. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Fragnelli, Vito & Marina, Maria Erminia, 2003. "A fair procedure in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 75-85, August.

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