Cost allocation in shortest path games

Abstract.

A class of cooperative games arising from shortest path problems is defined. These shortest path games are totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; first, 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. The core and the bargaining sets of Davis-Maschler and Mas-Colell are shown to coincide. 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 payoff vectors in the strong Nash equilibria of the associated noncooperative shortest path game.