Martin Hoefer, Lars Olbrich, Alexander Skopalik
We study taxes in the well-known game theoretic traffic model due to Wardrop. Given a network and a subset of edges, on which we can impose taxes, the problem is to find taxes inducing an equilibrium flow of minimal network-wide latency cost. If all edges are taxable, then marginal cost pricing is known to induce the socially optimal flow for arbitrary multi-commodity networks. In contrast, if only a strict subset of edges is taxable, we show NP-hardness of finding optimal taxes for general networks with linear latency functions and two commodities. On the positive side, for single-commodity networks with parallel links and linear latency function, we provide a polynomial time algorithm for finding optimal taxes.
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