局部紧空间上偏好关系的构造理论

Douglas S. Bridges
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引用次数: 19

摘要

本文在严格构造框架下,研究了局部紧空间X上的偏好关系(严格弱阶),以及从X到X的连续效用函数(序同构)对这种关系的表示。当X是RN的一个局部紧的凸子集时,给出了用算法根据参数求效用函数值的必要条件。这些条件挑选出一类可接受的偏好关系,我们对此进行了详细的研究。最后给出了将效用函数赋给允许偏好关系的过程的算法连续性的一些结果。本文的工作可以看作是偏好和效用理论的递归发展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The constructive theory of preference relations on a locally compact space

This paper, which is written within a rigorously constructive framework, deals with preference relations (strict weak orders) on a locally compact space X, and with the representation of such relations by continuous utility functions (order isomorphisms) from X into ℝ. Necessary conditions are given for finding the values of a utility function algorithmically in terms of the parameters when X is a locally compact, convex subset of RN. These conditions single out the class of admissible preference relations, which are investigated in some detail. The paper concludes with some results on the algorithmic continuity of the process which assigns utility functions to admissible preference relations.

The work of this paper can be regarded as a recursive development of preference and utility theory.

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