Games in Normal Form

Chapters 1 and 2 provided the background for the remainder of this book. In this chapter, we consider normal-form games, a representation of noncooperative games, to model strategic situations when the players move simultaneously. We study different solution concepts for such a class of games and discuss their existence and computation. We begin this chapter with some examples. This is one of the most commonly used examples to illustrate basic ideas of game theory. In the prisoner’s dilemma, two prisoners are being convicted for a crime. Lacking credible evidence, the authorities question the prisoners independently to know whether they committed the crime. No preplay communication is allowed. Each prisoner has two possible actions: \(\{C,D\}\) —confess the crime (C) and do not confess (D). This is also a bimatrix game, and the payoff matrix is shown in Fig. 3.1.