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On the manipulability of allocation rules through endowment augmentation

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  • Thomson, William

Abstract

We formulate and study the requirement on an allocation rule that no agent should be able to benefit by artificially augmenting their endowment. This can be either through simply exaggeration or through a transfer of resources from outside of the current trading partners, resources that have to be returned after the rule is applied and the agent has received their assignment. We show that the Walrasian rule is not “augmentation-proof” even on standard domains. More seriously, no efficient selection from the individual-endowments lower bounds correspondence, or from the no-envy correspondence, or from the egalitarian-equivalent correspondence is augmentation-proof. These impossibilities hold even when preferences are homothetic, and even if the agent cannot augment their endowment by more than an arbitrarily small proportion of the resources they truly own.

Suggested Citation

  • Thomson, William, 2024. "On the manipulability of allocation rules through endowment augmentation," Games and Economic Behavior, Elsevier, vol. 146(C), pages 91-104.
  • Handle: RePEc:eee:gamebe:v:146:y:2024:i:c:p:91-104
    DOI: 10.1016/j.geb.2024.04.012
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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.
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    4. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
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    8. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
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    12. Shin Sato, 2013. "Strategy-proofness and the reluctance to make large lies: the case of weak orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 479-494, February.
    13. 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.
    14. Klaus, Bettina & Dimitrov, Dinko & Haake, Claus-Jochen, 2006. "Bundling in exchange markets with indivisible goods," Economics Letters, Elsevier, vol. 93(1), pages 106-110, October.
    15. William Thomson, 2011. "Borrowing-Proofness of the Lindahl Rule in Kolm Triangle Economies," Studies in Choice and Welfare, in: Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), Social Ethics and Normative Economics, pages 169-191, Springer.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Aumann, R. J. & Peleg, B., 1974. "A note on Gale's example," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 209-211, August.
    21. William Thomson, 2023. "On the shape of Pareto sets in Edgeworth box economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 181-190, October.
    22. 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.
    23. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
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    More about this item

    Keywords

    Augmentation-proofness; Endowment lower bound; No-envy; Egalitarian-equivalence;
    All these keywords.

    JEL classification:

    • D39 - Microeconomics - - Distribution - - - Other
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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