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3 Problem 2 Consider a situation that there are two students, 1 and 2, who are planning to do some joint project. To do it, they need to purchase a PC, which is either of Mac-type and Windows-type. To implement the joint project, it is convenient for them to purchase the same type of PCs together. Moreover, because of the characteristic of the joint project they have considered, jointing using Mac-type PC is more suited to the project than using Windows-type. Note that for each of 1 and 2, his/her available action is to purchase 'Mac' or 'Windows'. Therefore, for 1, his strategy set is specified by A1 5 {mac, windows}. Likewise, for 2, her strategy set is specied by A2 5 {mac, windows}. Then, a strategic-form game (N; 11,142; (n1,n2)) with N = {1,2} is specied by: for the payoff function u; : A; x A2 > R of the player 1, we have: n; (mac, mac) = a, n1 (windows, mac) = ,6, n1 (mac, windows) = 7, in (windows, windows) = :5; while for the payoff function u; : A; x A2 > R of the player 2, we have: n2 (mac, mac) = 6, a; (windows, mac) = 5, n2 (mac, windows) = C, 11.2 (windows, windows) = n, where a, ,6, T, and 6 are real numbers satisfying a > ,3 = 6 > 1/; and e, E, C, and n are also real numbers satisfying 6 = n > E = C. Given this game, answer the following questions: (1) Describe the game matrix of this game. (2) Show whether there exists a dominant strategy equilibrium in this game or not, and moreover, if yes, what a dominant strategy equilibrium of the game is. (3) Show whether there exists a dominated Nash equilibrium in this game or not, and moreover, if yes, what a dominated Nash equilibrium of the game is