Game theory is the mathematical study of interaction among independent, self-interested agents. It has been applied to disciplines as diverse as economics (historically, its main area of application), political science, biology, psychology, linguistics—and computer science. In this chapter we will concentrate on what has become the dominant branch of game theory, called noncooperative game theory, and specifically on normal-form games, a canonical representation in this discipline.

As an aside, the name “noncooperative game theory” could be misleading, since it may suggest that the theory applies exclusively to situations in which the interests of different agents conflict. This is not the case, although it is fair to say that the theory is most interesting in such situations. By the same token, in Chapter 12 we will see that coalitional game theory (also known as cooperative game theory) does not apply only in situations in which the interests of the agents align with each other. The essential difference between the two branches is that in noncooperative game theory the basic modeling unit is the individual (including his beliefs, preferences, and possible actions) while in coalitional game theory the basic modeling unit is the group. We will return to that later in Chapter 12, but for now let us proceed with the individualistic approach.

Self-interested agents

What does it mean to say that agents are self-interested? It does not necessarily mean that they want to cause harm to each other, or even that they care only about themselves.