Timescale standard to discriminate between hyperbolic and exponential discounting and construction of a nonadditive discounting model
Timescale standard to discriminate between hyperbolic and exponential discounting and construction of a nonadditive discounting model
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区分双曲线贴现和指数贴现的时间尺度标准以及非加性贴现模型的构建
DOI：
10.1007/s11238-022-09916-6
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发表时间：
2022
影响因子：
0.8
通讯作者：
Matsushita Yutaka
中科院分区：
文献类型：
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作者：
Awano Naoyuki;Hayashi Yuki;Matsushita Yutaka
在假设人类的时间知觉在跨期选择中被扭曲的前提下，本研究在公理测量的框架下构建了时间量表。首先，提出了确定时间尺度形式的条件(一次或二次齐性)，以确定双曲函数和指数函数中哪个更适合于模拟人们的贴现。一度的同质性意味着主观时延是用幂标度来度量的，其贴现函数是幂指数型的；而二度的同质性意味着主观时滞是用对数标度来度量的，其贴现函数是双曲型的。其次，给出了一个能够反映次可加折扣和超可加折扣的模型的构造方法。提供了一种非交换和非关联的级联运算来生成由细分持续时间组成的时间串，该时间串结合了具有细分持续时间的重复延迟的影响。通过在配备有广义时间尺度的指数模型中替换这些字符串来产生折扣模型，并且次可加性或超可加性的确定取决于通过非交换和非结合运算的乘积的折扣函数值分别小于或大于通过通常的扩展结构的运算的乘积的折扣函数值。
Under the presupposition that human time perception is distorted in intertemporal choice, this study constructs a time scale in the framework of axiomatic measurement. First, the conditions (homogeneity of degree one or two) to identify the form of a time scale are proposed so that one can determine whether the hyperbolic or exponential is a more suitable function for modeling people’s discounting. Homogeneity of degree one implies that subjective time delay is measured by a power scale and its discount function becomes a power-exponential type, whereas homogeneity of degree two implies that subjective time delay is measured by a log scale and its discount function becomes a hyperbolic type. Second, a method is shown for constructing a model that can reflect subadditive and superadditive discounting. A non-commutative and non-associative concatenation operation is provided to generate a time string consisting of subdivided durations that incorporates the effect of repeated delay with a subdivided duration. The discounting model is yielded by substituting these strings in an exponential model equipped with a generalized time scale, and the determination of subadditivity or superadditivity depends on whether the discount function value of a product by the non-commutative and non-associative operation is, respectively, smaller or greater than that of a product by an operation of the usual extensive structure.