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Consider a three firm oligopoly in which the market demand for the homogeneous good is given...

Consider a three firm oligopoly in which the market demand for the homogeneous good is given by q = 24 - p, and costs are zero. Suppose firm 1 and 2 simultaneously pick their output, and then firm 3, observing these choices, picks its output (i.e. two “leaders”, one “follower”). Find the subgame perfect equilibrium for this model. Also show that the outcome in which each firm produces 6 units of output can be supported as Nash equilibrium, but not as a subgame perfect equilibrium outcome.

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