  We present a general framework to model strategic aspects and stable and fair
resource allocations in networks via variants and generalizations of path
coalitional games. In these games, a coalition of edges or vertices is
successful if it can enable an s-t path. We present polynomial-time algorithms
to compute and verify least core payoffs of cost-based generalizations of path
coalitional games and their duals, thereby settling a number of open problems.
The least core payoffs of path coalitional games are completely characterized
and a polynomial-time algorithm for computing the nucleolus of edge path
coalitional games on undirected series-parallel graphs is presented.
