3. (a) Consider the following payoff matrix: L Player 2 R 1,1 4,2 Player 1 T M B 2,0 3.4 1,3 1.2 0.2 2,3 3,0 (0) Compute pure strategy NE and mixed-strategy NE of the following 2-player game in normal form. (Hint: players will never play their dominated strategy). Draw the best response function for this game. (15 marks) () Write out and solve for equilibrium strategies of the extensive form game with the same payoffs, but in which row player moves first and column player observe the row player's move. (6 marks) b) Prove that if a simultaneous-move game has a dominant strategy equilibrium, then this is the only Nash equilibrium for the game. (6 marks) 4. Suppose there are two firms, firm B and firm N, producing complementary goods. The demand curve for each firm is described as follows: Q8 = Z-PB-PN and QN = Z - PN-PB Assume further that each firm faces a constant unit cost of production, c = 0. a) Write the payoff functions for the firms. Find the Nash equilibrium strategies. (8 marks) b) Find the subgame perfect Nash equilibrium strategies in the case that B moves first, N chooses its price after observing the price charged by B. (8 marks)