An Approximation Algorithm for Stackelberg Network Pricing

Details An Approximation Algorithm for Stackelberg Network Pricing An Approximation Algorithm for Stackelberg Network Pricing

2004-09-27

arxiv.org/abs/cs/0409054v1

Computer Science

Computer Science and Game Theory

38 pages

Scientific paper

We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly NP-hard. We then provide a polynomial time algorithm with a worst-case precision guarantee of ${1/2}\log_2 m_T+1$, where $m_T$ denotes the number of toll arcs. Finally we show that the approximation is tight with respect to a natural relaxation by constructing a family of instances for which the relaxation gap is reached.

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