Game Theory

2.a) Find the best response functions of the private firm, x, = b, (x, ) and of the public firm, x, = b. (x, ). 2.b) Depict the best response functions in a graph. For simplicity, restrict your analysis to three cases: 0 = 0, 0 =.5, and 0=1. Explain what happens to the public firm's best-response function and the resulting equilibrium as O increases. (How does the resulting equilibrium compare to the standard Cournot model where both firms only care about profits ( 0 = 0 )? 2.c) Calculate the equilibrium quantities for both firms. Find aggregate output in equilibrium. What happens to total output when 0 increases? 2.d) Now assume that the private firm moves first and the public firm, moves second. Determine the equilibrium outputs in this game as well as aggregate output. 2.e) Calculate the socially optimal level of output (for when both firms move simultaneously) and compare it with the equilibrium outcome you obtained in (3.c) and (3.d)