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Monotonicity and Envyfree Assignments

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  • Alkan, Ahmet

Abstract

Given any problem involving assignment of indivisible objects and a sum of money among individuals, there is an efficient envy-free allocation (namely the minmax money allocation) which can be extended monotonically to a new efficient envyfree allocation for any object added or individual removed, and another (the maximin value allocation) extendable similarly for any object removed or person added. Still, the efficient envyfree solution is largely incompatible with the resource and population monotonicity axioms: The minmax money and maxmin value allocations are unique in being extendable.

Suggested Citation

  • Alkan, Ahmet, 1994. "Monotonicity and Envyfree Assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 605-616, May.
    • Handle: RePEc:spr:joecth:v:4:y:1994:i:4:p:605-16
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    Citations

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    Cited by:

    1. Rodrigo A. Velez, 2017. "Sharing an increase of the rent fairly," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 59-80, January.
    2. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, 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. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona School of Economics.
    5. Maniquet, François, 2008. "Social orderings for the assignment of indivisible objects," Journal of Economic Theory, Elsevier, vol. 143(1), pages 199-215, November.
    6. Bevia, Carmen, 1996. "Population monotonicity in economies with one indivisible good," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 125-137, October.
    7. Eun Jeong Heo & Sunghoon Hong & Youngsub Chun, 2021. "Kidney exchange with immunosuppressants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 1-19, July.
    8. 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.
    9. Yengin, Duygu, 2013. "Population monotonic and strategy-proof mechanisms respecting welfare lower bounds," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 389-397.
    10. Emre Doğan, 2021. "Population monotonicity in fair division of multiple indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 361-376, June.
    11. Bevia, Carmen, 1996. "Population monotonicity in a general model with indivisible goods," Economics Letters, Elsevier, vol. 50(1), pages 91-97, January.
    12. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    13. Yengin, Duygu & Chun, Youngsub, 2020. "No-envy, solidarity, and strategy-proofness in the queueing problem," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 87-97.
    14. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    15. Velez, Rodrigo A., 2015. "Sincere and sophisticated players in an equal-income market," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1114-1129.
    16. Sertel, Murat R. & Yildiz, Muhamet, 1999. "Double-edged population monotonicity of Walrasian equilibrium--a note on the nature of competition," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 235-251, May.

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