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Allocation rules are very generally vulnerable to the strategic withholding of endowments

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  • William Thomson

    (University of Rochester - River Campus)

Abstract

An allocation rule is “withholding-proof" if no agent ever benefits from withholding some of the resources they own, their final bundle consisting of what the rule assigns to them together with whatever they withheld. It was known that on the “classical" domain of continuous, monotone, and convex preferences, no rule is efficient and withholding-proof (Postlewaite, Rev Econ Stud 46:255–262, 1979). We show that this disappointing news persists under the simultaneous imposition of the following three restrictions: (i) the domain only consists of classical and homothetic preferences; (iii) when an agent withholds some of their endowment, they only recover a percentage of what they withhold, no matter how close to 0 that percentage is; (iii) rules are required to satisfy any of the central punctual requirements of fairness, the individual-endowments lower bounds, no-envy in trades (adapted from Tinbergen, Redelijke Inkomensverdeling, Second Edition. N.D. DeGulden Pers, Haarlem, 1953, and Foley, Yale Economic Essays 7:45–98, 1967) and egalitarian-equivalence in trades (adapted from Pazner and Schmeidler, Quart J Econ 92:671–687, 1978 and Schmeidler and Vind, Econometrica 40:637–642, 1972).

Suggested Citation

  • William Thomson, 2024. "Allocation rules are very generally vulnerable to the strategic withholding of endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 791-809, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00897-0
    DOI: 10.1007/s00182-024-00897-0
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    References listed on IDEAS

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    1. Murat Atlamaz & Bettina Klaus, 2007. "Manipulation via Endowments in Exchange Markets with Indivisible Goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 1-18, January.
    2. Andrew Postlewaite, 1979. "Manipulation via Endowments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 255-262.
    3. John E. Roemer, 1986. "Equality of Resources Implies Equality of Welfare," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 751-784.
    4. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 769-783.
    5. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    6. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 373-394.
    7. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
    8. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
    9. William Thomson, 2014. "New variable-population paradoxes for resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 255-277, February.
    10. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
    11. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(4), pages 671-687.
    12. Chichilnisky, Graciela & Thomson, William, 1987. "The walrasian mechanism from equal division is not monotonic with respect to variations in the number of consumers," Journal of Public Economics, Elsevier, vol. 32(1), pages 119-124, February.
    13. Hyungjun Kim, 2004. "Population monotonic rules for fair allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 59-70, August.
    14. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    15. Chun, Youngsub & Thomson, William, 1988. "Monotonicity properties of bargaining solutions when applied to economics," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 11-27, February.
    16. Christopher P. Chambers & Takashi Hayashi, 2020. "Can everyone benefit from economic integration?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(3), pages 821-833, June.
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