The Stag Hunt is a story that became a game. The game is a prototype of social contract. The Stag Hunt does not have the same melodramatic quality as the Prisoner's Dilemma. In the Stag Hunt, what is rational for one player to choose depends on his beliefs about what the other will choose. Both stag hunting and hare hunting are equilibria. That is just to say that it is best to hunt stag if the other player hunts stag and it is best to hunt hare if the other player hunts hare. The two mentioned games, Prisoner's Dilemma and the Stag Hunt, are not unrelated. Considerations raised by both Hobbes and Hume can show that a seeming Prisoner's Dilemma is really a Stag Hunt. Suppose that Prisoner's Dilemma is repeated. Then actions on one play may affect partner's actions on other plays, and considerations of reputation may assume an importance that they cannot have if there is no repetition.
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