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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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/407913 |
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| _version_ | 1849414085686329344 |
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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. |
| format | Article |
| id | doaj-art-70dc01e34f4049969aee53179f673cc6 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| 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 |