Border-collision bifurcations in a model of Braess paradox

Arianna Dal Forno and Ugo Merlone

Mathematics and Computers in Simulation (MATCOM), 2013, vol. 87, issue C, 1-18

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.

Keywords: Braess paradox; Ternary games; Discontinuous 2-dim maps; Border-collision bifurcations; Periodicity tongues (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:87:y:2013:i:c:p:1-18

DOI: 10.1016/j.matcom.2012.12.001

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