Problem 1(b) is only required for those enrolled in the graduate level course (i.e., those taking...

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Problem 1(b) is only required for those enrolled in the graduate level course (i.e., those taking 705 rather than 405). 1. Consider the Cournot oligopoly game defined in class with a > c> 0. (a) For the two-player case, find the total production Q that maximizes the firms' joint profit (i.e., the sum of their individual net profits). Call (1Q,Q) the collusive outcome of the game. Explain why the collusive outcome is not a Nash equilibrium. (b) For the n-player case, prove that in any Nash equilibrium q every firm produces the same quantity (9₁ = 92 = ... = 9n). (c) Find the Nash equilibria in the n-player case. What happens to the price-per-unit, P(Q), in equilibrium as n → ∞o? Problem 1(b) is only required for those enrolled in the graduate level course (i.e., those taking 705 rather than 405). 1. Consider the Cournot oligopoly game defined in class with a > c> 0. (a) For the two-player case, find the total production Q that maximizes the firms' joint profit (i.e., the sum of their individual net profits). Call (1Q,Q) the collusive outcome of the game. Explain why the collusive outcome is not a Nash equilibrium. (b) For the n-player case, prove that in any Nash equilibrium q every firm produces the same quantity (9₁ = 92 = ... = 9n). (c) Find the Nash equilibria in the n-player case. What happens to the price-per-unit, P(Q), in equilibrium as n → ∞o?

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