### 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 |
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Pages (from-to) | 26-39 |

Number of pages | 14 |

Journal | Games and Economic Behavior |

Volume | 86 |

DOIs | |

Publication status | Published - 2014 Jul |

### Keywords

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

### ASJC Scopus subject areas

- Finance
- Economics and Econometrics