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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 is influenced 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 properties are also explored. Finally, some numerical examples are presented and a comprehensive sensitivity analysis on the critical parameters is conducted to show the efficiency of the proposed model and solution method.

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