递归效用与汤普森聚合器,Ii:递归效用表示的唯一性

R. Becker, J. P. Rincón-Zapatero
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引用次数: 1

摘要

我们重新考虑了Mari-nacci和Montrucchio[30]提出的汤普森聚合器理论。我们证明了给定一个Thompson聚合器,Koopmans方程具有唯一的效用函数解。唯一性只存在于商品空间正锥的内部。我们证明了Koopmans算子是一个0凹算子。我们利用Liang等人的一般充分条件验证了这一点。先前发表的结果将收缩映射定理的变体应用于具有汤普森度量的可能效用函数的空间。凹算子方法作用于具有范数拓扑的可能效用函数空间。我们的方法结合了顺序和度量结构来展示与现有文献不同的独特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Recursive Utility and Thompson Aggregators, Ii: Uniqueness of the Recursive Utility Representation
We reconsider the theory of Thompson aggregators proposed by Mari-nacci and Montrucchio [30]. We demonstrate the Koopmans equation has a unique utility function solution given a Thompson aggregator. Uniqueness holds only on the interior of the commodity spaces positive cone. Our proof veries the Koopmans operator is a u0 concave operator. We verify this using general sufficient conditions due to Liang, et al [28]. Previous published results apply variants of the contraction mapping theorem to the space of possibly utility functions endowed with the Thompson metric. Concave operator methods work on the possible utility function space with its norm topology. Our approach combines order and metric structures to demonstrate uniqueness differently than in the existing literature.
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