Prisoners' Dilemma
Two culprits X and Y are taken prisoner as crime suspects. They are imprisoned in separate rooms, and are not allowed to talk to each other. However, to prove that they indeed committed the crime, the police will have to solicit a confession from either one against the other. The various payoffs, all of which are jail terms in number of years (hence the payoffs are shown as negative numbers) are given below. Here, the first number is the payoff for X, and the second is the payoff for Y (e.g, the bottom left hand quadrant has a payoff of -10,0 which means a jail term of 10 years for X and 0 years for Y).
As you can see, it is in the best interest of both prisoners that they keep silent, in which case they can't be implicated for the major crime and are given a minor punishment of 6 months (1/2 year) each. Both the prisoners know this, but can they trust the other? Let's put ourselves in the shoes of X. X knows that if he keeps quiet and Y also keeps quiet, both of them will be out of jail in 6 months. However, if Y talks and testifies against X, the bottom left hand quadrant shows that Y will go free and X will have to go to jail for 10 years. Can X trust Y? Definitely not, if X applies his intelligence; for it can't afford to take that chance. Similarly, Y is in the same situation, and can't trust that X will keep silent! In other words, both will testify against each other and both will go to jail for 5 years each.
Business Application: In the context of competitive businesses, each firm will do the best it can given what its competitors would do. In the real world, "repeated gaming" might allow for firms to "collude", which is the equivalent of both prisoners keeping silent in the example above and going to jail for only 6 months as opposed to five years. Also see Integrative Bargaining in our section on Business Concepts, and also the Pareto Negotiation Frontier in the Advanced Frameworks section.
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