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Impossibility Results for Parametrized Notions of Efficiency and Strategyproofness in Exchange Economies

  • Wonki Jo Cho

We study a standard model of exchange economies with individual endowments. It is well known that no rule is individually rational, efficient, and strategy-proof. In order to quantify the extent of this impossibility, we parametrize axioms on allocation rules. Given an axiom A, a parametrization of A is a continuum of axioms {δ-A}δ∈[0,1] such that (i) δ-A is equivalent to A if and only if δ=1; (ii) δ-A is vacuous if and only if δ=0; and (iii) for each pair δ,δ′∈[0,1] with δ<δ′, δ′-A implies δ-A. Thus, as δ decreases from 1 to 0, δ-A weakens monotonically, eventually to a vacuous requirement. We consider two parametrizations {δ-efficiency}δ∈[0,1] and {δ-strategy-proofness}δ∈[0,1], and investigate their compatibility with individual rationality for the class of two-agent economies defined on the linear preference domain. We show that (i) for each δ∈(0,1], no rule is individually rational, δ-efficient, and strategy-proof; and (ii) for each δ∈(0,1], no rule is individually rational, efficient, and δ-strategy-proof.

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 1314.

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Date of creation: 2013
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Handle: RePEc:man:sespap:1314
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  1. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
  2. Andrew Postlewaite, 1979. "Manipulation via Endowments," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 255-262.
  3. David A. Smith, 1999. "Manipulability measures of common social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 639-661.
  4. Maus,Stefan & Peters,Hans & Storcken,Ton, 2004. "Minimal Manipulability: Anonymity and Unanimity," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Biung-Ghi Ju, 2003. "Strategy-proofness versus efficiency in exchange economies: General domain properties and applications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 73-93, 08.
  6. Aumann, R. J. & Peleg, B., 1974. "A note on Gale's example," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 209-211, August.
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