Basic Elements of Static and Dynamic Games

Abstract

Since our approach in this book is based on (dynamic) game theory, it will be useful to present at the outset some of the basic notions of zero-sum game theory and some general results on the existence and characterization of saddle points. We first discuss, in the next section, static zero-sum games, that is, games where the actions of the players are selected independently of each other; in this case we also say that the players’ strategies are constants. We then discuss in Sections 2.2 and 2.3 some general properties of dynamic games (with possibly nonlinear dynamics), first in the discrete time and then in the continuous time, with the latter class of games known also as differential games. In both cases we also introduce the important notions of representation of a strategy, strong time consistency, and noise insensitivity.