| 有理数概率下的效用表示定理 |
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| 引用本文： | 刘常青,郭耀煌.有理数概率下的效用表示定理[J].成都理工大学学报(自然科学版),2001,28(2):199-203. |
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| 作者姓名： | 刘常青 郭耀煌 |
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| 作者单位： | 西南交通大学经济管理学院, |
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| 基金项目： | 国家自然科学基金;79870034; |
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| 摘 要： | Von Neum ann- Morgenstern的期望效用理论假设对所有的抽奖 (c1 ,p;c2 ,1- p) (以概率 p抽得结果 c1 ,以概率 1- p抽得结果 c2 )的偏好序在所有实数 p(0≤ p≤ 1)均有意义 ;而且期望效用理论基于一组公理 ,从而保证效用函数的存在性和正线性变换意义下的唯一性。然而 ,当概率为无理数时 ,对于抽奖就难以给出直观的解释 ,J.C.Shepherdson首先研究了基于有理数概率度量的效用理论。作者提出一组有理数概率下效用函数存在的公理 ,并证明该公理体系下的效用表示定理。
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| 关 键 词： | 乘子集 M-混和集 效用函数 有理数概率 |
| 文章编号： | 1005-9539(2001)02-0199-05 |
| 修稿时间： | 2000年12月14日 |
UTILITY REPRESENTATION WITH RATIONAL PROBABILITIES |
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| LIU Chang-qing,GUO Yao-huang.UTILITY REPRESENTATION WITH RATIONAL PROBABILITIES[J].Journal of Chengdu University of Technology: Sci & Technol Ed,2001,28(2):199-203. |
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| Authors: | LIU Chang-qing GUO Yao-huang |
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| Abstract: | The expected utility theory of Von Neumann-Morgenstern assumes that a preference order is defined for all lotteries (c1, p; c2, 1-p) (c1 with probability p, c2 with probability 1-p) for all real p, 0≤p≤1. And the expected utility theory is based on a set of axioms that assure the existence and uniqueness (up to a positive affine transformation) of utility for all real probability. But when the probability p is irrational, it is hard to interpret the lottery intuitively. J.C.Shepherdson first studies the utility theory based on rational probabilities. This paper puts forward a set of axioms and proves the existence and uniqueness of utility function with rational probabilities on the set of axioms. |
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| Keywords: | multiplier set M mixture set utility function rational probability |
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