Border-collision bifurcations in a model of Braess paradox

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.

► The addiction of extra resources enriches the complexity of the dynamics. ► The Braess paradox is interpreted as a dynamical ternary choice problem. ► The dynamics is described by a piecewise linear map with a continuum of discontinuities. ► A geometrical and analytical analysis of the Braess paradox is provided. ► We provide the conditions for the existence of first degree tongues.