Differential stackelberg games and their application to dynamic pricing, production planning network design, and logistics

Recently, Stackelberg games have been employed by many economists who use game theory concepts to solve dynamic competitive service sector problems such as dynamic pricing, production planning, logistics, supply chain management, and transportation network flow prediction and control. Hence, Stackelberg games have become the focus of much research activity.;In this thesis, we provide a framework for studying player interaction based on the Stackelberg- Cournot-Nash behavioral assumption. We briefly review the classical theory of dynamic Stackelberg games, and show how the Nash equilibrium of a lower level problem may be better described by so-called differential variational inequalities (DVI). We also show that when each agent in the lower level problem is solving a stochastic optimal control with a linear quadratic form, the stochastic Nash equilibrium can be expressed as a Riccati system of equations. Both a DVI formulation and a Riccati system of equations may be used to express the solution of the lower level problem implicitly as a function of the upper level problem's controls. Hence, we are able to convert the bi-level optimization problem into a single-level problem. Furthermore, we study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. In the first model, we con- sider a Stackelberg game between a single carrier that acts as the leader and multiple shippers involved in a Nash competition. In the second model, we study the interaction between a supplier who is the leader and multiple retailers who are competing to sell a homogeneous commodity in a market when the market price evolves based on an Ito-type stochastic process.