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Inertia in binary choices: Continuity breaking and big-bang bifurcation points


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  • Gardini, Laura
  • Merlone, Ugo
  • Tramontana, Fabio


In several situations the consequences of an actor’s choices are also affected by the actions of other actors. This is one of the aspects which determines the complexity of social systems and make them behave as a whole. Systems characterized by such a trade-off between individual choices and collective behavior are ubiquitous and have been studied extensively in different fields. Schelling, in his seminal papers (1973, 1978), provided an interesting analysis of binary choice games with externalities. In this work we analyze some aspects of actor decisions. Specifically we shall see what are the consequences of assuming that switching decisions may also depend on how close to each other the payoffs are. By making explicit some of these aspects we are able to analyze the dynamics of the population where the actor decision process is made more explicit and also to characterize several interesting mathematical aspects which contribute to the complexity of the resulting dynamics. As we shall see, several kinds of dynamic behaviors may occur, characterized by cyclic behaviors (attracting cycles of any period may occur), also associated with new kinds of bifurcations, called big-bang bifurcation points, leading to the so-called period increment bifurcation structure or to the period adding bifurcation structure.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 80 (2011)
Issue (Month): 1 ()
Pages: 153-167

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Handle: RePEc:eee:jeborg:v:80:y:2011:i:1:p:153-167

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Keywords: Binary choices; Switching systems; Piecewise smooth systems; Border collision bifurcations big-bang bifurcation;

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  1. Galam, Serge, 2003. "Modelling rumors: the no plane Pentagon French hoax case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 571-580.
  2. Bischi, Gian-Italo & Merlone, Ugo, 2010. "Binary choices in small and large groups: A unified model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 843-853.
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Cited by:
  1. Dal Forno, Arianna & Merlone, Ugo, 2013. "Border-collision bifurcations in a model of Braess paradox," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 1-18.
  2. Ugo Merlone & Daren Sandbank & Ferenc Szidarovszky, 2013. "Equilibria analysis in social dilemma games with Skinnerian agents," Mind and Society: Cognitive Studies in Economics and Social Sciences, Fondazione Rosselli, vol. 12(2), pages 219-233, November.
  3. Ingrid Kubin & Laura Gardini, 2013. "Border collision bifurcations in boom and bust cycles," Journal of Evolutionary Economics, Springer, vol. 23(4), pages 811-829, September.


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