An interesting thought experiment in group versus individual rationality. Two co-conspirators are arrested and questioned separately (no communication allowed!) about a crime they have committed. Each has the choice to snitch on the other (defect), or to keep quiet (cooperate; this is from the point of view of the prisoners, not the authorities). No matter what your fellow prisoner does, it is to your advantage to defect; in game-theoretical terms, this is a dominant strategy for both players. However, this behaviour (always defecting) leads to worse payoffs for everyone than if everyone had cooperated. An example is:
- If you snitch (defect) and your comrade keeps mum (cooperates), e gets five years and you get off with a slap on the wrist.
- If your comrade snitches and you keep mum, you get five years and e gets off scot-free.
- If you both keep quiet, you each get one year.
- If you both snitch, you each get three years.
Supposing your fellow prisoner keeps quiet, snitching gets you zero years in prison as opposed to one. Supposing your fellow prisoner is going to rat on you, ratting on em gets you three years as opposed to five. Thus, assuming you have no way of collaborating, it is in your best interest to defect; it will always improve your outcome, no matter what your opponent choses. However, if both players follow the obvious strategy, the results (three years each in prison) will be worse than if each player had remained silent. In game-theoretical terms, this happens because the prisoner's dilemma game is at a Nash equilibrium when both players defect. However, the single Nash equilibrium is not a pareto optimal outcome. That is, it is possible to provide a solution that decreases or leaves fixed everyone's jail time (that is, always cooperating). This is what makes it a `dilemma'.
The tragedy of the commons, a related game, there are two Nash equilibria (always defect and `minimally effective cooperation'), the latter of which is pareto optimal. The problem here is that, in real-world situations, it is usually impossible to immediately tell when the point of `minimally effective cooperation' has been reached.
Also related is Wolf's dilemma, which involves any number of people. Each person may choose to press or not to press a button. If no one pushes the button, everyone gets $1000 (insert your own amount here). If anyone presses the button, then everyone who presses the button will get $10, and everyone else will get $0. Transitional Man discusses a form of the Prisoner's dilemma which uses a similar payoff matrix. Unlike the original (Flood, Dresher, and Tucker) prisoner's dilemma, there is not necessarily a dominant strategy here---the optimal strategy, according to Nash equilibria, is often a mixed strategy, with weights depending on the payoff values. This still does not yield a pareto optimal outcome, so the dilemma still exists.
Finally, there are single-player games related to the prisoner's dilemma. One example is: you are connected to a pain-causing electrical circuit and are given a control to vary the current; the amount of pain is directly proportional to the current. You begin at zero, and every day have the option to either increase the current by 1 microamp (an indetectable amount) and receive $1000; or leave the current where it is and receive $0. On any single day, it makes sense to accept the $1000---the increase in pain is unnoticeable. However, in the long run, continuing to do this will eventually lead to an unbearable amount of pain---which many people would trade their entire fortune to eliminate. This is similar to the tragedy of the commons, with the participants being yourself at different points of time. Minimally effective cooperation (pareto optimal and a Nash equilibrium) here is to find the highest current level that is indefinitely bearable, receive the money (defect) until you reach that level, and keep the current constant (cooperate) after that. As with the tragedy of the commons, the problem is in realising and stopping when you reach that level.
For a site with mathematical and historical information on the prisoner's dilemma and variants such as the
tragedy of the commons, see http://plato.stanford.edu/entries/prisoner-dilemma/ .