Impulsivity in Binary Choices and the Emergence of Periodicity

Binary choice games with externalities, as those described by Schelling (1973, 1978), have been recently modelled as discrete dynamical systems (Bischi and Merlone, 2009). In this paper we discuss the dynamic behavior in the case in which agents are impulsive; that is; they decide to switch their ch...

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Main Authors: Gian Italo Bischi, Laura Gardini, Ugo Merlone
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/407913
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author Gian Italo Bischi
Laura Gardini
Ugo Merlone
author_facet Gian Italo Bischi
Laura Gardini
Ugo Merlone
author_sort Gian Italo Bischi
collection DOAJ
description Binary choice games with externalities, as those described by Schelling (1973, 1978), have been recently modelled as discrete dynamical systems (Bischi and Merlone, 2009). In this paper we discuss the dynamic behavior in the case in which agents are impulsive; that is; they decide to switch their choices even when the difference between payoffs is extremely small. This particular case can be seen as a limiting case of the original model and can be formalized as a piecewise linear discontinuous map. We analyze the dynamic behavior of this map, characterized by the presence of stable periodic cycles of any period that appear and disappear through border-collision bifurcations. After a numerical exploration, we study the conditions for the creation and the destruction of periodic cycles, as well as the analytic expressions of the bifurcation curves.
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spelling doaj-art-70dc01e34f4049969aee53179f673cc62025-08-20T03:33:57ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/407913407913Impulsivity in Binary Choices and the Emergence of PeriodicityGian Italo Bischi0Laura Gardini1Ugo Merlone2Department of Economics and Quantitative Methods, Faculty of Economics and Business, University of Urbino, 61029 Urbino, ItalyDepartment of Economics and Quantitative Methods, Faculty of Economics and Business, University of Urbino, 61029 Urbino, ItalyDepartment of of Statistics and Applied Mathematics "de Castro", Corso Unione Sovietica 218 bis, 10134 Torino, ItalyBinary choice games with externalities, as those described by Schelling (1973, 1978), have been recently modelled as discrete dynamical systems (Bischi and Merlone, 2009). In this paper we discuss the dynamic behavior in the case in which agents are impulsive; that is; they decide to switch their choices even when the difference between payoffs is extremely small. This particular case can be seen as a limiting case of the original model and can be formalized as a piecewise linear discontinuous map. We analyze the dynamic behavior of this map, characterized by the presence of stable periodic cycles of any period that appear and disappear through border-collision bifurcations. After a numerical exploration, we study the conditions for the creation and the destruction of periodic cycles, as well as the analytic expressions of the bifurcation curves.http://dx.doi.org/10.1155/2009/407913
spellingShingle Gian Italo Bischi
Laura Gardini
Ugo Merlone
Impulsivity in Binary Choices and the Emergence of Periodicity
Discrete Dynamics in Nature and Society
title Impulsivity in Binary Choices and the Emergence of Periodicity
title_full Impulsivity in Binary Choices and the Emergence of Periodicity
title_fullStr Impulsivity in Binary Choices and the Emergence of Periodicity
title_full_unstemmed Impulsivity in Binary Choices and the Emergence of Periodicity
title_short Impulsivity in Binary Choices and the Emergence of Periodicity
title_sort impulsivity in binary choices and the emergence of periodicity
url http://dx.doi.org/10.1155/2009/407913
work_keys_str_mv AT gianitalobischi impulsivityinbinarychoicesandtheemergenceofperiodicity
AT lauragardini impulsivityinbinarychoicesandtheemergenceofperiodicity
AT ugomerlone impulsivityinbinarychoicesandtheemergenceofperiodicity