Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 407913, 22 pages
doi:10.1155/2009/407913
Research Article

Impulsivity in Binary Choices and the Emergence of Periodicity

Gian Italo Bischi,1 Laura Gardini,1 and Ugo Merlone2

1Department of Economics and Quantitative Methods, Faculty of Economics and Business, University of Urbino, 61029 Urbino, Italy
2Department of of Statistics and Applied Mathematics "de Castro", Corso Unione Sovietica 218 bis, 10134 Torino, Italy

Received 17 March 2009; Accepted 15 June 2009

Academic Editor: Xue-Zhong He

Copyright © 2009 Gian Italo Bischi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.