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Follower payoffs in symmetric duopoly games

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This paper compares the leader and follower payoffs in a duopoly game, as they arise in sequential play, with the Nash payoffs in simultaneous play. If the game is symmetric, has a unique symmetric Nash equilibrium, and players’ payoffs are monotonic in the opponent’s choice along their own best reply function, then the follower payoff is either higher than the leader payoff, or lower than even in the simultaneous game. As a possible interpretation, endogenous timing in such games is difficult since the players either want to move both second or both first.

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