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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 345795, 12 pages
Research Article

Dynamics in Braess Paradox with Nonimpulsive Commuters

1Department of Economics and Statistics “Cognetti de Martiis,” University of Torino, 10153 Torino, Italy
2Department of Psychology, University of Torino, 10124 Torino, Italy
3DESP, University of Urbino “Carlo Bo,” 61026 Urbino, Italy
4IST, University of Stuttgart, 70550 Stuttgart, Germany

Received 16 May 2014; Accepted 27 July 2014

Academic Editor: Nikos I. Karachalios

Copyright © 2015 Arianna Dal Forno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In Braess paradox the addiction of an extra resource creates a social dilemma in which the individual rationality leads to collective irrationality. In the literature, the dynamics has been analyzed when considering impulsive commuters, i.e., those who switch choice regardless of the actual difference between costs. We analyze a dynamical version of the paradox with nonimpulsive commuters, who change road proportionally to the cost difference. When only two roads are available, we provide a rigorous proof of the existence of a unique fixed point showing that it is globally attracting even if locally unstable. When a new road is added the system becomes discontinuous and two-dimensional. We prove that still a unique fixed point exists, and its global attractivity is numerically evidenced, also when the fixed point is locally unstable. Our analysis adds a new insight in the understanding of dynamics in social dilemma.