4. Cournot Competition, Collusion and Dominant Strategies. Two companies compete in the market for videogames, Sonar and YSquare. Demand for videogames is Q=140-P and the two firms have the same constant marginal costs equal to 20. Fixed costs are zero and the two firms compete in quantities. a. Find the best response functions of the two firms and draw them in a graph. b. Find the Cournot equilibrium quantities, price and profits. C. What would be instead the equilibrium price and the output sold if this market were perfectly competitive? Calculate the deadweight loss of the Cournot equilibrium with respect to the perfectly competitive outcome. d. Now suppose that the two firms collude. What are the collusion quantities, price and profits? Calculate the deadweight loss of the collusive outcome with respect to perfect competition. Compare it with the deadweight loss of the Cournot equilibrium. e. Consider now the following two alternative strategies. Both firms can simultaneously decide to produce either the Cournot quantity or half the monopoly (collusive) quantity. Construct the payoff matrix indicating each firm's profits for all possible combinations of outputs by both firms. Is there a dominant strategy? What will be the equilibrium choice for the two firms and therefore the outcome of their competitive interaction? Explain your results in detail