The classical prisoner's dilemma
You and your accomplice in a serious crime are arrested by the police. However, the police only have enough evidence to convict you both for a minor offence. You are separated and offered a deal:
Assume all you want is to minimise your own jail term. You have two options: to say nothing, or to confess and betray your accomplice. The outcome depends on what your accomplice does and unfortunately, you don't know what he’ll do. Even if you could talk to him, could you trust him? If you choose...
You stay silent / He stays silent
Both serve 6 months for minor offence.
If you both decide to stay quiet, you would both be able to get out in 6 months. In a situation with a payoff matrix like the prisoner's dilemma, individual selfish decisions are not automatically best if viewed from the perspective of the group as a whole. This result presents the group (here, you and your accomplice) with a win-win outcome.
You confess / He stays silent
He serves 10 years; you go free.
If you expect your accomplice will choose to co-operate and stay quiet, the optimal choice for you would be to defect, as this means you get to go free immediately, while your accomplice lingers in jail for 10 years.
You stay silent / He confesses
He goes free; you serve 10 years.
If you stay silent but your accomplice confesses, this is the worst outcome for you. If you expect your accomplice will choose to defect, your best choice is to defect as well, since then at least you can be spared the full 10 years serving time and have to sit out only 5 years, while your accomplice does the same.
You confess / He confesses
Both serve 5 years.
The naively selfish reasoning that it is better for you to defect and confess is flawed; you’d both end up in jail for 5 years. With sophisticated selfish reasoning, if you count on your accomplice to co-operate and say nothing, it would be best for you to defect and confess. You would go free. But, knowing this, he would defect too, so it would be best if you both co-operated. And so on. This is the core of dilemma.
Non-zero-sum situations are those in which one person's benefit does not necessarily come at the expense of someone else. Conversely, in zero-sum situations, one person must lose in order that another can win. Non-zero-sum situations exist where the supply of a resource is not fixed or limited. It is a case of building a resource rather than dividing it between players. In some non-zero-sum situations (like negotiation between a mentor and mentee), a person can benefit only when others benefit as well.
The more complex societies get and the more complex the networks of interdependence within and beyond community and national borders get, the more people are forced in their own interests to find non-zero-sum solutions. That is, win-win solutions instead of win-lose solutions. Because we find as our interdependence increases that, on the whole, we do better when other people do better as well – so we have to find ways that we can all win; we have to accommodate each other.Bill Clinton, Wired interview, December 2000.