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

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  • Wonki Jo Cho

Abstract

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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Suggested Citation

  • Wonki Jo Cho, 2013. "Impossibility Results for Parametrized Notions of Efficiency and Strategyproofness in Exchange Economies," The School of Economics Discussion Paper Series 1314, Economics, The University of Manchester.
  • Handle: RePEc:man:sespap:1314
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    Cited by:

    1. Harless, Patrick, 2015. "Solidarity with respect to small changes in preferences in public good economies with single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 81-86.
    2. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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