A congestion network features a source point and a number of agents; and the cost of shipping units of demand between any two vertices is given by an edge-specific cost function. Given the matrix of cost functions and the agents’ demands, one must firstly find a cost-minimizing network (efficiency) and secondly share the cost of this optimal network between the agents in a way that is stable (no subgroup of agents has incentives to secede). In the respective cases of minimum cost spanning trees (constant costs), shortest-path problems (linear costs), and convex congestion networks (convex costs), the efficiency issue has been solved namely by Prim (1957), Dijkstra (1959) and Klein (1967). However, with the exception of minimum cost spanning trees, not much has been done in terms of finding sensible cost sharing rules for network problems. We address this issue in a series of papers; and for each of these problems we propose a procedure allowing to find cost allocations that are stable and fair. Potential applications include cost (or surplus) sharing for public transportation systems, communication networks, electricity grids, and pipelines.
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