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An algorithm for envy-free allocations in an economy with indivisible objects and money

Author

Listed:
  • Flip Klijn

    () (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000LE Tilburg, The Netherlands)

Abstract

This paper studies envy-free allocations for economies with indivisible objects, quasi-linear utility functions, and an amount of money. We give a polynomially bounded algorithm for finding envy-free allocations. Connectedness of envy-graphs, which are used in the algorithm, characterizes the extreme points of the polytopes of sidepayments corresponding with envy-free allocations.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:17:y:2000:i:2:p:201-215
    Note: Received: 22 October 1997/Accepted: 19 January 1999
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    Citations

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    Cited by:

    1. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    2. Klijn, Flip & Tijs, Stef & Hamers, Herbert, 2000. "Balancedness of permutation games and envy-free allocations in indivisible good economies," Economics Letters, Elsevier, vol. 69(3), pages 323-326, December.
    3. Ehlers, Lars & Svensson, Lars-Gunnar & Andersson, Tommy, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
    4. Onur Kesten & Ayşe Yazıcı, 2012. "The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 463-488, June.
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. 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.
    11. 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.
    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. 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.
    14. Chang, Carlos M. & Montes, Edith, 2014. "An Optimization Approach Applied to Fair Division Transportation Funding Allocation Models," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 53(1).
    15. 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.
    16. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    17. repec:spr:grdene:v:11:y:2002:i:5:d:10.1023_a:1020485018300 is not listed on IDEAS
    18. Haake, Claus-Jochen & Raith, Matthias G. & Su, Francis Edward, 2017. "Bidding for envy freeness," Center for Mathematical Economics Working Papers 311, Center for Mathematical Economics, Bielefeld University.
    19. 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.
    20. Meertens, Marc & Potters, Jos & Reijnierse, Hans, 2002. "Envy-free and Pareto efficient allocations in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 223-233, December.

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