(An) adaptive algorithm for differential game in dynamic advertising model

Abstract

This thesis presents an alternative method for generating a near-optimal closed-loop solution to a non-zero sum perfect information differential game. The alternative method utilizes a concept of fundamental matrix and yields the nearoptimal closed-loop solution which is generated by periodically updating the solutions of the two-point boundary-value problem. The resulting updated open-loop control is used between updating intervals. The advertising differential game model is based on a non-price competition between a new-entering company and its target company. Several numerical examples are solved. The results show that the adaptitive algorithm can be used as an efficient tool to solve the generalized differential game model in which one player can take advantage of the other``s non-optimal play.