Characterizing the Shapley Value in Fixed-Route Traveling Salesman Problems with Appointments

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to ?nd a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We intro- duce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley Value in this class using a property which requires that sponsors do not bene?t from mergers, or splitting into a set of sponsors.