## Abstract

For every integrable allocation (X_{1}, X_{2}, ..., X_{n}) of a random endowment Y=Σ_{i}^{=1/n}X_{i} among n agents, there is another allocation (X_{1}*, X_{2}*, ..., X_{n}*) such that for every 1≤i≤n, X_{i}* is a nondecreasing function of Y (or, (X_{1}*, X_{2}*, ..., X_{n}*) are co-monotone) and X_{i}* dominates X_{i} by Second Degree Dominance. If (X_{1}*, X_{2}*, ..., X_{n}*) is a co-monotone allocation of Y=Σ_{i}^{=1/n}X_{i}*, then for every 1≤i≤n, Y is more dispersed than X_{i}* in the sense of the Bickel and Lehmann stochastic order. To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.

Original language | English |
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Pages (from-to) | 97-106 |

Number of pages | 10 |

Journal | Annals of Operations Research |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1994 |

## Keywords

- Bickel-Lehmann dispersion
- Co-monotonicity