Attitude toward imprecise information
Attitude toward imprecise information
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DOI：
10.1016/j.jet.2007.09.002
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发表时间：
2008-05-01
影响因子：
1.6
通讯作者：
Vergnaud, J. -C.
中科院分区：
文献类型：
--
作者：
Gajdos, T.;Hayashi, T.;Vergnaud, J. -C.
本文提出了一个不确定性决策的公理化模型，它包含了客观但不精确的信息。信息被假定为概率-可能性集合的形式，即状态空间上的概率测度的集合P。决策者被告知，真正的概率定律存在于P中，并被假设为对形式为（P，f）的对进行排序，其中f是将状态映射为结果的行为。密钥表示结果提供最大最小期望效用（MEU），其中最小运算符在一组概率先验上变化-正如吉尔博亚和Schmeidler的MEU表示结果[具有非唯一先验的最大最小期望效用，J.Math.Econ.18（1989）141-153]。然而，与MEU表示不同的是，这里的表示还提供了一个映射phi，它将描述可用信息的概率-可能性集与揭示的先验集联系起来。映射phi表示决策者的态度不精确的信息：根据我们的公理，一组代表先验构成的概率可能性集的选择。这允许当所选集合是单例时的期望效用和当所选集合与概率-可能性集合相同时的极端悲观，即，phi是恒等映射。我们定义了一个概念，比较不精确的厌恶，并表明它的特点是包含的集合显示的概率分布，不管效用函数，捕捉风险的态度。我们还确定了一个明确的态度，不精确的基础通常对冲公理。最后，我们的特点，根据额外的公理，一个更具体的功能形式，其中一组选定的概率分布是通过（i）解决的“平均值”的概率可能性集，和（ii）收缩的概率可能性集的平均值的程度由偏好决定。(c)2007年爱思唯尔公司All rights reserved.
This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability-possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P, f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors-just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153]. However, unlike the MEU representation, the representation here also delivers a mapping, phi, which links the probability-possibility set, describing the available information, to the set of revealed priors. The mapping phi is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability-possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability-possibility set, i.e., phi is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the "mean value" of the probability-possibility set, and (ii) shrinking the probability-possibility set toward the mean value to a degree determined by preferences. (c) 2007 Elsevier Inc. All rights reserved.