Abstract: A class of cooperative games arising from shortest path problems is de ned. These shortest path games are shown to be totally balanced and allow a populationmonotonic 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 payo vectors in the strong Nash equilibria of the associated noncooperative shortest path game.
Maintaining the assumption of s-veto players, Voorneveld and Grahn REF extended the shortest path game and proved that the core allocations coincide with the payoff vectors in the strong Nash equilibria of the associated non-cooperative shortest path game.
Cost Allocation in Shortest Path Games
Mathematical Methods of Operations Research
Computer Science Mathematics