Introduction and examples

In ordinary language, we speak of a “game” as a (generally amusing) process of interaction that involves a given population of individuals, is subject to some fixed rules, and has a prespecified collection of payoffs associated to every possible outcome. Here, the concept of a game mostly embodies the same idea. However, in contrast to the common use of this term, the kind of interaction to be studied may be far from amusing, as illustrated by the following example.

Consider the game usually known as the prisoner's dilemma (PD). It involves two individuals, labeled 1 and 2, who have been arrested on the suspicion of having committed jointly a certain crime. They are placed in separate cells and each of them is given the option by the prosecutor of providing enough evidence to incriminate the other. If only one of them chooses this option (i.e., “defects” on his partner), he is rewarded with freedom while the other individual is condemned to a stiff sentence of twelve years in prison. On the other hand, if both defect on (i.e., incriminate) each other, the available evidence leads to a rather long sentence for both of, say, ten years in prison. Finally, let us assume that if neither of them collaborates with the prosecutor (i.e., they both “cooperate” with each other), there is just basis for a relatively light sentence of one year for each.