A major difference between the Stag Hunt and the Prisoner's Dilemma is that:

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In the Prisoner's Dilemma, mutual defection is indeed the Nash equilibrium because it is the strategy that each player will choose, assuming the other player's best response, leading to a worse collective outcome. In contrast, the Stag Hunt has two equilibria: one where both players cooperate (hunt the stag) for a higher reward, and another where both defect (hunt the hare) for a lower but safer reward, highlighting the difference in the nature of strategic choices between the two games.

A Major Difference Between the Stag Hunt and the Prisoner's