Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies

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3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)26-39
Number of pages14
JournalGames and Economic Behavior
Volume86
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes

Fingerprint

Impossibility
Strategy-proofness
Exchange economy
Strategy-proof
Axioms
Allocation rules
Endowments
Compatibility
Axiom
Individual rationality

Keywords

  • Exchange economy
  • Individual rationality
  • δ-Efficiency
  • δ-Strategy-proofness

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

Cite this

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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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AB - 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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