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].

- 10.5.1 Game Trees
- 10.5.1.1 Determining a security plan
- 10.5.1.2 Computing a saddle point
- 10.5.1.3 Converting the tree to a single-stage game

- 10.5.2 Sequential Games on State Spaces

- 10.5.3 Other Sequential Games

Steven M LaValle 2020-08-14