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Impulsivity in Binary Choices and the Emergence of Periodicity


  • Gian Italo Bischi
  • Laura Gardini
  • Ugo Merlone


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.

Suggested Citation

  • Gian Italo Bischi & Laura Gardini & Ugo Merlone, 2009. "Impulsivity in Binary Choices and the Emergence of Periodicity," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-22, August.
  • Handle: RePEc:hin:jnddns:407913
    DOI: 10.1155/2009/407913

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    Cited by:

    1. Radi, Davide & Gardini, Laura & Avrutin, Viktor, 2014. "The role of constraints in a segregation model: The symmetric case," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 103-119.
    2. Radi, Davide & Gardini, Laura, 2015. "Entry limitations and heterogeneous tolerances in a Schelling-like segregation model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 130-144.
    3. Dal Forno, Arianna & Gardini, Laura & Merlone, Ugo, 2012. "Ternary choices in repeated games and border collision bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 294-305.

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