1/ (Cournot's duopoly game with linear inverse demand and a fixed cost)
Find the Nash equilibrium of Cournot's game when there are 2 firms, the inverse demand function is given by equation
P(Q) = a - Q if Q < a ; P(Q) = 0 if Q > a
The cost function of each firm i is given by Ci(qi) = 0 if qi = 0 ; Ci(qi) = f + c.qi if qi > 0 , where c > 0, f > 0, and c < a. (Note that the fixed cost f affects only the firm's decision of whether to operate; it does not affect the output a firm wishes to produce if it wishes to operate.)