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

•We determine the PoA of atomic splittable traffic equilibria with elastic demand.•The PoA of elastic demand case is larger than that of fixed demand case.•The demands’ elastic can have a negative effect on equilibrium solutions.•There exit optimal toll in general network, atomic players, elastic demand case.•The PoA for elastic demands case can reduce to 3/2 under the optimal toll scheme.

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.