2) Now consider the following variant of a Cournot duopoly

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2) Now consider the following variant of a Cournot duopoly. Suppose that firm 1 already exists in the industry and firm 2 is considering whether to enter. If firm 2 stays out, then firm 1 observes this and is a monopolist, choosing their level of production, q₁ accordingly. If firm 2 decides to enter (or go ”in”), then it pays a cost f and firm 1 again observes this choice. The two firms then choose their levels of production as Cournot duopolists, q₁ and q₂. Suppose that the inverse demand function and the cost of production functions are as in class.

That is, let C_i (q_i) = cq_i and let

P(q₁ + q₂) =

a - q1 – q2 if q1 + q2 £ a

0                 if q1 + q2 > a

 

(a) What are the action sets for each firm in this game?

(b) What are the strategy sets for each firm?

(c) Give the extensive form of this game.