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• W4311959451 abstract "In the 1990s, after a series of experiments, the behavioral psychologist and economist Daniel Kahneman and his colleagues formulated the following Peak-End evaluation rule: The remembered utility of pleasant or unpleasant episodes is accurately predicted by averaging the Peak (most intense value) of instant utility (or disutility) recorded during an episode and the instant utility recorded near the end of the experience, (D. Kahneman et al., 1997, QJE, p. 381). Hence, the simplest mathematical model for time evolution of the experienced utility function $u=u(t)$ can be given by the scalar differential equation $u'(t)=a u(t) + b max {u(s) : sin [t-h,t]}+f(t) (*),$ where $f$ represents exogenous stimuli, $h$ is the maximal duration of the experience, and $a, b in mathbb R$ are some averaging weights. In this work, we study equation $(*)$ and show that, for a range of parameters $a, b, h$ and a periodic sine-like term $f$, the dynamics of $(*)$ can be completely described in terms of an associated one-dimensional dynamical system generated by a piece-wise continuous map from a finite interval into itself. We illustrate our approach with two examples. In particular, we show that the hedonic utility $u(t)$ (`happiness') can exhibit chaotic behavior." @default.
• W4311959451 created "2023-01-03" @default.
• W4311959451 creator A5018186636 @default.
• W4311959451 creator A5063285153 @default.
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• W4311959451 date "2022-12-09" @default.
• W4311959451 modified "2023-10-03" @default.
• W4311959451 title "The peak-end rule and its dynamic realization through differential equations with maxima ^*" @default.
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• W4311959451 doi "https://doi.org/10.1088/1361-6544/aca50d" @default.
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