Strong Coalitional Structure in an Open Vehicle Routing Game

In the chapter it is investigated a special case of one-product open vehicle routing game, in which there is a central warehouse or wholesaler, several customers, who are considered to be players. Each player is placed in a node of the transportation network and is characterized by demand and distance to the warehouse. For such a problem a coalitional transportation game (CTG) is formalized. In such a game each customer (player) should rent a track to deliver goods from the central warehouse. It is assumed that all tracks have the same capacity. The players tend to minimize their transportation costs and totally supply their demands. A player may rent a vehicle alone, or chose a coalition of players to cooperate. In cooperation the players of coalitions find the shortest path form the central depot to all the player of coalition. Transportation costs are allocated between players according to the Nash arbitration scheme. Strong equilibrium which is stable against deviations of any coalition of players is found in a CTG. A computation procedure for strong equilibrium construction is proposed. Implementation of procedure is illustrated with a numerical example.