The peak-end rule and its dynamic realization through differential equations with maxima *

Author:

Trofymchuk Olena,Liz EduardoORCID,Trofimchuk Sergei

Abstract

Abstract In the 1990s, after a series of experiments, the behavioural 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 (Kahneman et al 1997 Q. J. Econ. 112 375–405). Based on this rule, we propose a mathematical model for the time evolution of the experienced utility function u = u ( t ) given by the scalar differential equation u ( t ) = a u ( t ) + b max { u ( s ) : s [ t h , t ] } + f ( t ) ( * ) , where f represents exogenous stimuli, h is the maximal duration of the experience, and a , b 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 representative examples. In particular, we show that the utility u(t) (e.g. ‘happiness’, interpreted as hedonic utility) can exhibit chaotic behaviour.

Funder

Fondo Nacional de Desarrollo Científico y Tecnológico

Publisher

IOP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A probabilistic model of relapse in drug addiction;Mathematical Biosciences;2024-06

2. On a conformable fractional differential equations with maxima;Malaya Journal of Matematik;2024-01-01

3. On a dynamical model of happiness;Mathematical Modelling of Natural Phenomena;2023

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