This question leads you through the computation of the negotiation equilibrium of the game described in Exercise 5.
(a) Start by analyzing the joint decisions made at the end of the game. For given production levels q1 and q2 , calculate the players' payoffs by using the standard bargaining solution. Write the payoffs in terms of arbitrary bargaining weights q1 and q2 .
(b) What are the firms' payoffs as functions of q1 and q2 for π1 = 1/2 and π2 = 1/2?
(c) While continuing to assume q1 = q2 = 1/2, solve the Cournot component of the model by using Nash equilibrium. Explain why there are multiple equilibria. How does the outcome compare with that of the basic Cournot model? Is the outcome efficient?
(d) Next suppose that p1 ≠ p2 . Find the players' Nash equilibrium output levels. Remember that q1 and q2 are required to be greater than or equal to 0. [Hint: The equilibrium is a corner solution, where at least one of the inequalities binds (q1 = 0 and/or q2 = 0), so calculus cannot be used.]
(e) Discuss how the firms' quantity choices depend on their bargaining weights and explain the difference between the results of parts (c) and (d).