Dynamic Game Theoretic Models in Marketing and Finance

by Wan, Wei

This dissertation deals with Differential Games (DG) and its application in general Market and Financial Market. It has three parts. Chapters 1-3 deal with optimal competition strategies for general product. I break up the normal product life cycle into three sub-stage life cycles, set up non-cooperative DG model for each sub-stage life cycle, derive optimality conditions for it, which in general is a set of Boundary Value Problems(BVPs) or Differential-Algebraic Equations(DAE), and design algorithms to solve it. One of the algorithms is based on full discretization, and is first-order convergent, the other algorithm is based on Shooting method and Random Perturbation technique, and belongs to quasi-Newton method. From the numerical results, I contrast the difference between open-loop and closed-loop controls. In Chapters 4-5, I set up Leader-Follower DG and cooperative DG for marketing competition. The motivation for these two special kinds of games comes from practical considerations. In Chapter 4, I use Calculus of Variation to derive a system of optimality conditions for Leader-Follower DG, and design an algorithm to solve it. The algorithm is random, and second order convergent. In Chapter 5, I set up cooperative DG model, and adopt Evolutionary Algorithm(EA) to solve the model. From the numerical results, I compare the above three kinds of DG, and draw practical guidelines. Chapter 6-7 deal with Stochastic Differential Games(SDG). In chapter 6, I set up SDG model for general market competition, and derive a set of optimality conditions using Dynamic Programming(DP). The set of optimality condition consists of Stochastic Partial Differential Equations(SPDE). Then, I design algorithm to solve the SPDE. In chapter 7, I extend SDE to financial marketing. I regard the pricing process as SDE between option seller and buyer, then I set up SDE model for option pricing. Finally, I derive optimality conditions for the pricing model.