Monday, November 14th, 2016
Cooperation is usually analysed in game theory by means of a non-zero-sum game called the Prisoner’s Dilemma.
Suppose that two criminals are arrested, but police can’t convict either on the primary charge, so they plan to sentence them to a year in jail on a lesser charge. Each of the prisoners, who can’t communicate with each other, are given the option of testifying against their partner. If they testify, and their partner remains silent, the partner gets three years and they go free. If they both testify, both get two. If both remain silent, they each get one.
The “dilemma” faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent.
The assumption is that you and your accomplice are rational. You want to have the shortest prison sentence possible and regardless of what your accomplice does, the rational choice is for you to betray your partner. The reason for this goes as follows. Suppose that he chooses to be silent. No jail is better than a year in jail, so you would betray him and testify. Now suppose that he chooses to betray you. Two months in jail is better than a year, so you would betray him and testify.
Your partner is a rational person as well and can reason in a similar way above. So he will choose the same option of betraying you. The result is that you will both serve two years in jail, an outcome that is among the worst for both of you.
A common view is that the puzzle illustrates a conflict between individual and group rationality. A group whose members pursue rational self-interest may all end up worse off than a group whose members act contrary to rational self-interest.
Summing-up: The prisoners’ dilemma is the best known strategy game in social science. By working in a rational manner, you end up with a worse result than had you cooperated with one another.