Cooperation is usually analysed in GameTheory by means of a non-zero-sum game called the "Prisoner's Dilemma".
The game got its name from the following hypothetical situation: imagine two criminals arrested under the suspicion of having committed a crime together. However, the police does not have sufficient proof in order to have them convicted. The two prisoners are isolated from each other, and the police visit each of them and offer a deal: the one who offers evidence against the other one will be freed. If none of them accepts the offer, they are in fact cooperating against the police, and both of them will get only a small punishment because of lack of proof. They both gain. However, if one of them betrays the other one, by confessing to the police, the defector will gain more, since he is freed; the one who remained silent, on the other hand, will receive the full punishment, since he did not help the police, and there is sufficient proof. If both betray, both will be punished, but less severely than if they had refused to talk. The dilemma resides in the fact that each prisoner has a choice between only two options, but cannot make a good decision without knowing what the other one will do. 
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The Prisoners' Dilemma has been and continues to be studied by people in a variety of disciplines, ranging from biology through sociology and public policy. Among its interesting characteristics are that it is a "non-zero-sum" game: the best strategy for a given player is often one that increases the payoff to one's partner as well. It has also been shown that there is no single "best" strategy: how to maximize one's own payoff depends on the strategy adopted by one's partner. One strategy called "TitForTat" is believed to be optimal under the widest possible set of partner strategies. ref
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