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New variable-population paradoxes for resource allocation


  • William Thomson

    (University of Rochester)


We identify previously unnoticed ways in which agents can strategically distort allocation rules, by affecting the set of “active” agents. (i) An agent withdraws with his endowment. (ii) He gives control of his endowment to someone else and withdraws. (iii) He invites someone in and let him use some of his endowment. (iv) He pre-delivers to some other agent the net trade that the rule would assign to that second agent if that second agent had participated. In (i) and (ii), he and his co-conspirator may end up controlling resources that allow them to reach higher welfare levels than they otherwise would. In (iii) and (iv), he may end up with a bundle that he prefers to the one he would have been assigned had he not engaged in the manipulation. We show that (i) the Walrasian rule is not “withdrawing-proof”, nor “endowments-merging–proof, nor “endowments-splitting–proof”, but that it is “pre-delivery–proof”, and that (ii) canonical selections from the egalitarian-equivalence-in-trades solutions satisfy none of the properties.

Suggested Citation

  • William Thomson, 2012. "New variable-population paradoxes for resource allocation," RCER Working Papers 575, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:575

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    References listed on IDEAS

    1. Andrew Postlewaite, 1979. "Manipulation via Endowments," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 255-262.
    2. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 43-62, February.
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    6. JU, Biung-Ghi & MORENO-TERNERO, Juan D., 2006. "Progressivity, inequality reduction and merging-proofness in taxation," CORE Discussion Papers 2006075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Gale, David, 1974. "Exchange equilibrium and coalitions : An example," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 63-66, March.
    8. Schmeidler, David & Vind, Karl, 1972. "Fair Net Trades," Econometrica, Econometric Society, vol. 40(4), pages 637-642, July.
    9. Sertel, Murat & Yildiz, Muhamet, 2004. "Core is manipulable via segmentation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 103-117, September.
    10. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    11. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, Oxford University Press, vol. 92(4), pages 671-687.
    12. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    13. Sonmez, Tayfun, 1999. "Can Pre-arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, Elsevier, vol. 86(1), pages 148-156, May.
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    Cited by:

    1. Nanyang Bu & Siwei Chen & William Thomson, 2014. "Merging and splitting endowments in object assignment problems," RCER Working Papers 587, University of Rochester - Center for Economic Research (RCER).

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    resource allocation rules; withdrawal-proofness; endowments-merging–proofness; endowments-splitting–proofness; pre-delivery–proofness;

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