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- Player 1 оооо Up (up, left) (up, right) (down, left) (down, right) None Down Player 2 Left P1: $15 P2: $15 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) P1: $12 P2: $18 Right P1:$11 P2: $16 P1: $13 P2: $13Player 2 Middle Left P1: $45 P1: $70 Up P2: $45 P2: $50 Player 1 P1: $50 P1: $60 Middle P2: $50 P2: $60 P1: $60 P1: $50 Down P2: $60 P2: $70 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, left) (up, middle) (up, right) (middle, left) (middle, middle) (middle, right) (down, left) (down, middle) (down, right) No equilibrium Right P1: $45 P2: $60 P1: $50 P2: $70 P1: $60 P2: $60Player 2 Left P1: $40 Player 1 Up P2: $0 P1: $44 Down P2:$44 In the game shown above, list all of the EFFICIENT Nash Equilibrium (please check ALL that apply) (up, left) (up, right) (down, left) (down, right) No efficient Nash Equilibrium Right P1:$1 P2: $1 P1: $0 P2: $40
- оооооооооо Player 1 (up, left) (up, middle) right) (up, (middle, left) (middle, middle) Up (middle, right) (down, left) (down, middle) (down, right) No equilibrium Middle In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) Down Left P1:$13 P2: $22 P1: $12 P2:$15 P1:$10 P2:$0 Player 2 Middle P1:$2 P2:$13 P1:$5 P2: $18 P1:$3 P2: $0 Right P1: $22 P2:$21 Pl: $31 P2:$7 P1:$34 P2:$1Player 1 O (up, left) In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, right) ☐ (down, left) Up (down, right) None Down Player 2 Left P1: $8 P2: $7 P1: $6 P2:$4 Right P1:$14 P2: $9 P1: $15 P2: $3Consider the Normal Form Game characterized in the following figure: P1 \ P2 A1 A2 A3 A4 B1 B2 B3 B4 (-1,1) (0,0) (1,-1) (2,0) (-2,-2) (2,7) (-1,-1) (-1,1) (5,7) (3,5) (0,0) (0,8) (0,3) (-1,-1) (10,2) (0,0) Which is the set of rationalizable actions? O (A2, A4)x(B2, B3) O (A1, A2)x(B1, B2, B4) O (A1, A3)x(B1, B4) O (A1, A3, A4}x{B1, B3)
- Up ооооо Down Player 1 Up No EFFICIENT equilibrium exists Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) P1 gets $15 P2 gets $25Consider the Normal Form Game characterized in the following figure: P1 \ P2 b1 b2 b3 a1 (1,2) (0,1) (0,3) a2 (3,-1) (1,1) (-1,0) a3 (2,2) (1,-1) (3,0) a4 (-5,1) (-1,0) (-3,-2) a5 (-3,3) (3,0) (2,4) What is the set of actions of player 1? O la 1, a2, a3, a4, a5) O (b1,b2, b3} O {a2, a3, a4) O (bl, b2}Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.
- 3. Three politicians are voting on whether to allow themselves a salary increase of $ 3,500 per year. If they vote in favour of a raise, then they lose some public support, costing them each $ 1,500 per year. The salary increase passes if two or more politicians vote in favour of it. What is this game’s Nash equilibrium (or equilibria)? Explain. There is no need to draw a payoff matrix. (20%• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.
