### 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 language | English |
---|---|

Pages (from-to) | 26-39 |

Number of pages | 14 |

Journal | Games and Economic Behavior |

Volume | 86 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Finance
- Economics and Econometrics

### Cite this

**Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies.** / Cho, Wonki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies

AU - Cho, Wonki

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

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.

KW - Exchange economy

KW - Individual rationality

KW - δ-Efficiency

KW - δ-Strategy-proofness

UR - http://www.scopus.com/inward/record.url?scp=84897444685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897444685&partnerID=8YFLogxK

U2 - 10.1016/j.geb.2014.03.003

DO - 10.1016/j.geb.2014.03.003

M3 - Article

AN - SCOPUS:84897444685

VL - 86

SP - 26

EP - 39

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

ER -