10.5 Sequential Game Theory

So far in the chapter, the sequential decision-making process has only involved a game against nature. In this section, other decision makers are introduced to the game. The single-stage games and their equilibrium concepts from Sections 9.3 and 9.4 will be extended into a sequence of games. Section 10.5.1 introduces sequential zero-sum games that are represented using game trees, which help visualize the concepts. Section 10.5.2 covers sequential zero-sum games using the state-space representation. Section 10.5.3 briefly covers extensions to other games, including nonzero-sum games and games that involve nature. The formulations in this section will be called sequential game theory. Another common name for them is dynamic game theory [59]. If there is a continuum of stages, which is briefly considered in Section 13.5, then differential game theory is obtained [59,477,783,985].