In the Prisoner's Dilemma, why didn't the prisoners simply agree to keep their mouths shut?
Definition: A commitment problem is a situation in which people cannot achieve their goals because of an inability to make credible threats or promises.
If both players in the Prisoner's Dilemma could make binding promise to remain silent, both would be assured of a shorter sentence. But once they were in separate interrogation rooms, without knowledge of what the other player was going to do, their dominant strategy became clear: confess.
How have criminals attempted to change the payoffs in the Prisoner's Dilemma, which is a simplification of a real world problem that criminals face?
The "mafia" or "Cosa Nostra" has attempted to change the payoffs through their code of omerta (vow of silence), under which anyone who provides evidence against a fellow mob member is killed in a painful way (and perhaps their family members also harmed). Criminals, in general, in general have created a system in which confessors who inform on their partners are called "rats," "stool pigeons" and other names and can be physically harmed. With such credible threats, prisoners will not assume that their payoff from confessing is always better than the payoff from remaining silent. Thus, if the threats are successful, the game matrix is transformed to one in which the dominant strategy is to remain silent.
Definition: A commitment device is a way of changing incentives so as to make otherwise empty threats or promises credible.
A commitment device is typically an institutional innovation designed to change the payoffs so that dominant strategy is socially optimal as well as privately optimal. Much of developments of society and culture can be viewed as attempts to create commitment devices to ensure that societies can achieve better outcomes in which costs and benefits are interdependent.
The logic of commitment devices explains the adoption of military arms control agreements, in which opponents sign an enforceable pledge to curtail weapons spending (or wire their computer systems to generate a situation of "mutually assured destruction" in the case of limited nuclear attack). It also explains why our societies make rules that enforce cooperation and contributions to the public goods (follow the laws, pay your taxes, don't generate substantial external costs to your neighbors, etc.). We recognize that we're better off curtailing our self-interest.
Of course, humans (and other species) have shown that Prisoner Dilemma-like problems can be solved without resort to external enforcement. Culture can provide "psychological incentives" that can create preferences for cooperation and distastes for defection. For example, concerns about fairness and feelings of guilt can influence the choices that people make. In some cases in which there is external enforcement, psychological incentives can be as strong or stronger. Consider the case of omerta again: the actual vow that criminals make has less to do with punishment and more to do with the absence of honor associated with informing on one's "family" members. Thus providing evidence against one's compatriots is considered a loss of honor, which for some people is a fate worse than death.
Example - Culture as a Commitment Device
Imagine that you are a member of a society in which each member chooses to be honest or dishonest when interacting with others. The game matrix below characterizes the players, the strategies and the payoffs (in this game the probability that someone would know you were dishonest and punish you is so small that it is unimportant).
If you and everyone else in your society are rational, self-interested individuals, what will be the equilibrium outcome in this game? Act dishonestly is a dominant strategy for everyone.
Now imagine the same society, but imagine that everyone in this society (including you) believes in a place called Heaven and a place called Hell. An all-powerful being observes the behavior of every member of this society and sends Honest people to Heaven when they die and Dishonest people to Hell when they die. Everyone in the society prefers Heaven to Hell.
If you and everyone else in your society are rational, self-interested individuals, what will be the equilibrium outcome in this game? Act honestly is a dominant strategy for everyone.
Other examples of commitment devices: tipping in restaurants even when you'll never return to it; how laws banning cigarette advertising on TV may have helped cigarette companies.