Cost allocation in shortest path games

A class of cooperative games arising from shortest path problems is deened. These shortest path games are shown to be totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; rst, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs into account by considering the costs of the second best alternative and that rewards players who are crucial to the construction of the shortest path. Finally, noncooperative games arising from shortest path problems are introduced, in which players make bids or claims on paths. The core allocations of the cooperative shortest path game coincide with the payoo vectors in the strong Nash equilibria of the associated noncooperative shortest path game. Nash equilibrium.