Bounding the inefficiency of atomic splittable selfish traffic equilibria with elastic demands

We determine the exact upper bound of the inefficiency of atomic splittable selfish traffic equilibria with elastic travel demand with and without road pricing. In the previous results, only pseudo-approximation bound were obtained for this case. By comparison, we also conclude that the traffic equilibrium with elastic demand may be worse than the corresponding fixed demand case, which implying that the demands’ elastic can have a negative effect on the quality of equilibrium solutions. Finally, we propose a road pricing mechanism. We prove that there are optimal tolls in general network, atomic players and elastic travel demand setting.