A particularly important game in game theory. It is a non-zero-sum game in which both players face an incentive not to cooperate with each other, even though the optimal outcome for both can be achieved only through cooperation.
(Dwayne Benjamin, Toronto PPG 1002H)
To understand this game, imagine two prisoners who were partners in a crime being questioned in separate rooms. Each prisoner has a choice of confessing to the crime and implicating the other or, he can deny his participation. If only one prisoner confesses, he goes free and his partner his punished with one year in jail. If both prisoners deny participating in the crime, they will both be held on a technicality and released in a month. If both prisoners confess, they are both held for three months.
Now, imagine that you are one of the prisoners in this situation. If your partner denies committing the crime, you are better off confessing since you will serve no time instead of a month. If your partner confesses, you are still better of confessing since you will serve three months instead of a year. No matter what your partner does, you are better off confessing to the crime. This result in a Nash equilibrium, but the result is inefficient for the pair of criminals taken together. The outcome, which produces the most utility of the pair of criminals, is for both players to deny their participation. This outcome would result in each criminal serving one month of jail time. However, because defecting is the dominant strategy, the result that game theory predicts will occur is that both prisoners will confess, resulting in each prisoner serving three months. Because they cannot coordinate their actions, both players are left with dominant strategies, which produce a socially undesirable outcome.