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Border-collision bifurcations in a model of Braess paradox

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  • Dal Forno, Arianna
  • Merlone, Ugo

Abstract

In Braess paradox adding an extra resource, and therefore an extra available choice, enriches the complexity of the game from a dynamic perspective. The analysis of the cycles and the bifurcations helps to visualize how this complexity changes, in a quite new way with respect to what is provided by the so far literature. We derive the conditions for the creation and the destruction of periodic cycles, as well as the analytical expressions of the bifurcation conditions, by studying the occurrence of border-collision bifurcations. We are also able to give a proof of the relation between the cost of the new resource and the existence of cycles of any given period, and also of the coexistence of equilibria, adding the path dependence to the problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:87:y:2013:i:c:p:1-18
    DOI: 10.1016/j.matcom.2012.12.001
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    Cited by:

    1. Ugo Merlone & Daren Sandbank & Ferenc Szidarovszky, 2013. "Equilibria analysis in social dilemma games with Skinnerian agents," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 12(2), pages 219-233, November.
    2. Arianna Dal Forno & Ugo Merlone, 2019. "Heterogeneous Society in Binary Choices with Externalities," Dynamic Games and Applications, Springer, vol. 9(2), pages 433-457, June.
    3. Ugo Merlone & Daren R. Sandbank & Ferenc Szidarovszky, 2012. "Systematic Approach Ton-Person Social Dilemma Games: Classification And Analysis," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-25.

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