Dynamic pricing in an urban freight environment

In this paper, we propose a dynamic, game theoretic model of dynamic pricing in an urban freight environment with three main entities: sellers, transporters and receivers. The sellers and transporters are modelled as non-cooperative Cournot-Nash agents. The sellers compete to capture receiver input factor demands, while the transporters compete to capture the transportation demand generated by the seller/receiver transactions. Each competing agent's extremal problem is formulated as an optimal control problem and the set of these coupled optimal control problems is transformed into a differential variational inequality representing the general Nash equilibrium problem. A nonlinear complementarity problem is also formulated and used to solve a numerical example.