A differential Stackelberg game for pricing on a freight transportation network with one dominant shipper and multiple oligopolistic carriers

This paper studies dynamic pricing and freight network equilibrium problem on a system consisting of one dominant producer called the shipper and multiple oligopolistic carriers who serve the shipper s origin-destination orders. The shipper sells a homogeneous commodity to spatially separated demand markets. The demand received by the shipper is price-sensitive, while the prices set for each market are inuenced by the pricing strategies of the oligopolistic carriers. We formulate the problem as a differential Stackelberg-Nash game to find the equilibrium production, price, and routing decisions over a planning horizon. A finite dimensional discretization method and a penalty function algorithm are proposed to solve the model. The existence and uniqueness of properties are also explored. Finally, some numerical examples are presented and a comprehensive sensitivity analysis on the critical parameters is conducted to show the e ciency of the proposed model and solution method.