On characterization of the core of lane covering games via dual solutions

The lane covering game (LCG) is a cooperative game where players cooperate to reduce the cost of cycles that cover their required lanes on a network. We discuss the possibilities/impossibilities of a complete characterization of the core via dual solutions in LCGs played among a collection of shippers, each with a number of service requirements along some lanes, and show that such a complete characterization is possible if each shipper has at most one service requirement.