This chapter introduces those concepts in static and dynamic game theory that are particularly relevant for the study of differential games, the theory of which will be presented in chapters 4 to 8. In this chapter we proceed in a somewhat informal way and do not attempt to render a precise mathematical representation of each and every concept. The main idea is to provide an understanding of what game theory is about, and we have chosen not to complicate matters by insisting on mathematical rigour. Those wishing to study more precise accounts of game theory should consult the references mentioned in section 2.4.

We start by discussing the distinction between noncooperative and cooperative games and offer some comments on game theoretic modelling. The chapter proceeds by presenting the two types of game theoretic models: the strategic form (or normal form) and the extensive form. We introduce fundamental concepts such as a player's strategy, the Nash equilibrium, the role of the information available to the players, and the concept of subgame perfectness. Finally, a brief presentation of a standard differential game model is given, postponing the detailed description to chapter 4.

Axioms of game theory

Game theory is concerned with the study of situations involving two or more decision makers (individuals, organizations, or governments). Decision makers are designated as players. The players often have partly conflicting interests and make individual or collective decisions.