Question 2 (4.5 marks) Consider a game of simultaneous moves between two players, Player A and Player B. Each player can choose between the same set of two actions: Action 1 and Action 2. The payoffs 2 are (3, 3) if they do not take the same action, and (2, 2) otherwise. a. Write down the payoff matrix of the game and find the best responses of each player to every possible action of the other player. (1 mark) Does Player A have a dominant strategy? What about Player B? (1/2 mark) b. Find all Nash Equilibria in pure strategies, if they exist. (1/2 mark) Does the Nash equilibrium always lead to a Pareto efficient outome in this game? Explain your answer. (1/2 mark) c. Suppose now that the payoff of Player 1 is 4 if both players play Action 1. Otherwise, the payoffs are the same as described above. Write the matix of the game and find all Nash equilibria in pure strategies, if they exist. (1 mark) Does Player A have a dominant strategy? What about Player B? (1/2 mark) Does the Nash equilibrium always lead to a Pareto efficient outome in this game? Explain your answer. (1/2 mark)