The Stackelberg outcome differs from the Cournot equilibrium because

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In a Stackelberg game, the first mover (leader) can commit to an output level. This means that the leader can choose an output level outside of its best-response function, which can give them an advantage over the other player (follower). In contrast, in a Cournot equilibrium, both firms choose their outputs simultaneously without knowing the other's strategy, resulting in a quantity that is a best-response to the other's quantity. This difference in strategic variables leads to different outcomes between the two games.

The Stackelberg Outcome Differs from the Cournot Equilibrium Because