1. Consider the following three-player game-frame (where ol, 02,...,018 are the possible outcomes): Player 2 D E F A 01 02 03 Player 1 04 05 06 07 08 09 Player 3: G Player 2 D E F A 010 011 012 Player 1 013 014 015 016 017 018 Player 3: H The players rank the outcomes as follows: 07,016 best 04, 014 015 013 best 01, 012 05, 014 09 Player 1: ol,07,ol1 05,013 Player 2: 06, 012 02 02, 08, 017 ol 1, 018 |03, 04,09,010,015,016,018 worst 06 03,08,010,017 worst 012 best 015 03, 06,016 Player 3: ol1 02, 07,014, 017 08, 010, 013, 018 ol, 04, 05,09 worst(a) For each player write a utility function that represents her ranking, using consecutive integers with 0 being the lowest. Use these utility functions to obtain a game based on the above game-frame. (b) For each player find all the strategies that are strictly dominated. (c) What do you get by applying the iterated deletion of strictly dominated strategies? (d) Are there any Nash equilibria?Q1.1 1(a) 1 Point For each player write a utility function that represents her ranking, using consecutive integers with 0 being the lowest. Use these utility functions to obtain a game based on the above game-frame. In this game, what are the payoffs associated with the strategy profile (B, D, H)? (what are the payoffs to each player when player 1 plays B, player 2 plays D, and player 3 plays H?) (8, 4, 2) (O (7.0,5) O (4,5,1) (8, 0,0) Q1.21(b) 1 Point For each player find all the strategies that are strictly dominated. Select all correct statements from the list below. [_] For Player 1, B is strictly dominated by C [_] For Player 2, D is strictly dominated by E [ ] None of the strategies are strictly dominated for any player [_] For Player 1, Ais strictly dominated by B [_] For Player 3, G is strictly dominated by H For Player 2, F is strictly dominated by E Q1.3 1(c) 1 Point What do you get by applying the iterated deletion of strictly dominated strategies? (Which strategy profiles remain after applying the iterated deletion of strictly dominated strategies?) O {(B, E, H) } O {(B,D,G), (B,E,G), (C,D,G), (C,E,G), (B,D,H), (B,E,H), (C,D,H), (C,E, H)} O {(B,D, H), (B,E,H), (C, D,H), (C,E, H) }\f2. Consider the following game (x and y can be any non-negative real numbers): Player 2 F G H A 2 , 4 2 , 3 0 , 3 B 2 , 1 3 , 4 1 , 0 C 3 , 2 4 , 2 2 ,y D x , 3 3 , 4 1 , 4 E 1 , 2 3 , 2 0 , 1 (a) For what values of x does Player I have a strictly dominant strategy? Name the strategy. (b) For what values of x does Player I have a weakly but not strictly dominant strategy? Name the strategy. (c) Are there values of y for which Player 2 has a weakly dominant strategy? (d) Find all the Nash equilibria when x = 1 and y = 2. (e) Find all the Nash equilibria when x = 4 and y = 2. (f) Let x = 4 and y = 3. What do you get when you apply the procedure of iterative elimination of strictly dominated strategies? Write explicitly the various steps of the elimination procedure.Q2.1 2(a) 1 Point For what values of & does Player 1 have a strictly dominant strategy? Write the number in the box below. Q2.2 2(b) 1 Point For what values of x does Player 1 have a weakly but not strictly dominant strategy? Write the number in the box below. Q2.3 2(c) 1 Point Are there values of y for which Player 2 has a weakly dominant strategy? ) Yes Q2.4 2(d) 1 Point Find all the Nash equilibria when x = 1 and y = 2. Select all correct options from the list below. (D, F) (B,H) O (C, F) O (C,H) (B,G) O (C,G) (D,H)Q2.5 2(e) 1 Point Find all the Nash equilibria when x = 4 and y = 2. Select all correct options from the list below. (D, F) (B,G) (D,H) (B,H) (C,G) O (C,H) O (C, F)Q2.6 2(f) 1 Point Let x =4 and y = 3. What do you get when you apply the procedure of iterative elimination of strictly dominated strategies? (Which strategy profiles remain after applying the iterated deletion of strictly dominated strategies?) O {(CH) O {(B,F)} O {C.G), (CH), (D,G), (D,H)}