7. Stackelberg Equilibria of Infinite Dynamic Games

7.1 Introduction This chapter is devoted to derivation of the Stackelberg solution in infinite dynamic games with fixed prescribed duration. The chapter starts with a treatment of dynamic games defined in discrete time and with the number of players restricted to two. Continuous-time counterparts of most of these results and possible extensions to many-player games are treated in the latter part. The next two sections, i.e., Sections 7.2 and 7.3, deal, respectively, with the Stackelberg solution under open-loop information and the feedback Stackelberg solution under CLPS information. These solutions are obtained using two standard techniques of optimal control theory, viz. the minimum principle and dynamic programming, respectively. Derivation of the (global) Stackelberg solution under the CLPS information pattern, however, requires a much more subtle analysis since all standard techniques and approaches of optimal control theory fail to provide the solution. Therefore, Section 7.4 is devoted exclusively to this topic and to elucidation of an indirect approach toward derivation of the closed-loop Stackelberg solution. This indirect approach is first introduced within the context of two scalar examples (cf. subsections 7.4.1 and 7.4.2), and then its application is extended to the class of two-person linear-quadratic dynamic games in subsection 7.4.3. There is a clear relationship with the theory of “incentives”, and this is the subject of subsection 7.4.4.