Many authors focus on the prisoner's dilemma as the game that best represents the problem of social cooperation.
Some authors believe that the the prison's dilemma is the wrong game to understand social cooperation.
The prototype of the social contract is instead the stag hunt.
The Stag Hunt
Rousseau, in A Discourse on Inequality:
"If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple..."
For a formalization in game theory of the stag hunt check HERE
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