Optimal pricing of capacitated networks

We address the algorithmic complexity of a profit maximization problem in capacitated, undirected networks. We are asked to price a set of $m$ capacitated network links to serve a set of $n$ potential customers. Each customer is interested in purchasing a network connection that is specified by a simple path in the network and has a maximum budget that we assume to be known to the seller. The goal is to decide which customers to serve, and to determine prices for all network links in order to maximize the total profit. We address this pricing problem in different network topologies. More specifically, we derive several results on the algorithmic complexity of this profit maximization problem, given that the network is either a path, a cycle, a tree, or a grid. Our results include approximation algorithms as well as inapproximability results.