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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.

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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 575.

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Length: 22 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:roc:rocher:575
Contact details of provider: Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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  1. Aumann, R. J. & Peleg, B., 1974. "A note on Gale's example," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 209-211, August.
  2. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
  3. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Sertel, Murat & Yildiz, Muhamet, 2004. "Core is manipulable via segmentation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 103-117, September.
  5. 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).
  6. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer, vol. 40(1), pages 43-62, February.
  7. SCHMEIDLER, David & VIND, Karl, . "Fair net trades," CORE Discussion Papers RP 131, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.
  9. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
  10. 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.
  11. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
  12. 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.
  13. Gale, David, 1974. "Exchange equilibrium and coalitions : An example," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 63-66, March.
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