1. Consider the following Cournot game: . There are n > 1 firms. . Firm i, i = 1, 2, ...,n, chooses an output qi E [0, co]. . The market inverse demand is P = a - bq, where a, b > 0 and q = 2 1 qi . Firm i's cost function is ci(qi) = cqi, where c > 0. (a) Solve the monopoly problem, in which there is only one firm in the market. (b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium. (c) Show that the Nash equilibrium of the above game covers cases of market outcomes arranging from monopoly (n = 1) to perfect competition (n - co).3. Use the best-response curves to nd all Nash equilibria (in both pure and mixed strate- gies) of the Battle of the Sexes game. 4. Find the Nash equilibrium of the following modied Rock-PaperScissors game: 0 When rock (R) beats scissors (S), the winner's payoff is 10 and the loser's payoff is 10. a When paper (P) beats rock, the Winner's payoff is 5 and the loser's payoff is 5. 0 When scissors beats paper, the winner's payoff is 2 and the loser's payoff is 2. o In case of ties, both players receive 0 payoff