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Timescale standard to discriminate between hyperbolic and exponential discounting and construction of a nonadditive discounting model

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  • Yutaka Matsushita

    (Kanazawa Institute of Technology)

Abstract

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.

Suggested Citation

  • Yutaka Matsushita, 2023. "Timescale standard to discriminate between hyperbolic and exponential discounting and construction of a nonadditive discounting model," Theory and Decision, Springer, vol. 95(1), pages 33-54, July.
  • Handle: RePEc:kap:theord:v:95:y:2023:i:1:d:10.1007_s11238-022-09916-6
    DOI: 10.1007/s11238-022-09916-6
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    References listed on IDEAS

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