Suppose two Cournot duopolists faced a linear(inverse) demandcurve p(q)=a-bq and each had constant(andidentical) marginal costs and no fixed costs so that the cost function of  firm i was c(qi)=cqi. Suppose that each firm could choose between three output levels:the collusive output(half the monopoly output), the best response to the collusive output and Cournot duopoly output. Write down the normal form game played by the two firms. Find all the Nashequilibria of this game.