Consider a Cournot game with three firms. Each firm produces a homogeneous good and faces linear demand of the form P(Q) = a-bQ, where Q = q1 +q2 +q3, and a and b are positive constants as per usual. Assume that all firms face zero costs (e.g. C(q) = 0).
a. For each firm, derive the best response function below. Show all work. You may not use the concept of symmetry to obtain your answer.
b. Solve for the Nash Equilibrium output of each firm. Show all work. You may not use the concept of symmetry to obtain your answer.
c. Solve for the equilibrium market price.
d. Solve for the equilibrium profits of each firm.