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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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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| ISSN: | 1026-0226 1607-887X |