The payoff table for a two person game is exhibited below. (0,0) (2,5) (5,5) (100,5) (5,5) (0,0) Use the sequential elimination of weakly dominated strategies to determine an outcome for the game. Show that the order in which strategies is eliminated makes a difference.
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- Iterative Elimination of Dominated Strategies Exercise 4.2 Consider the following normal form of a game. Use IEDS to reduce this game and find any Nash Equilibrium. X Y Z (60,50) (50,110) (70,90) (100,60) (70,70) (110,100) (110,70) (100,110) (40,40)Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1Consider again the normal form of the Prisoner's dilemma game. Determine any Nash Equilibrium. Player 2 R (-10,-10) (-1,-25) (-25,-1) (-3,-3) C Player 1 R
- Player 2 Cooperate (1,000, 1,000) Cheat Player 1 (400, 2,000) Cooperate Cheat (2,000, 400) (500, 500) The above payoff matrix is for two players, each with two strategies. What is the Nash equilibrium of this game? Cheat and Cooperate Cheat and Cheat Cooperate and Cooperate Cooperate and CheatTerry's payoff is the first number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [Select ] v and Kerry will [ [ Select ]Player 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. What is the Nash equilibrium in this game? Strategy 1 and Strategy A Strategy 2 and Strategy A Strategy 2 and Strategy B This game does not have a Nash equilibrium
- Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()A large group of players each guesses a number between 0 and 300. The winner is the person whose number is closest to three-fifth of the average guess. What is the Nash equilibrium? Will it be observed? What do you expect for the outcome of this game with next year's 203 class? (Considering that they have similar sophistication to your class but they have not covered game theory yet.)
- Player 2 1 2 3 1 (0,2) (1,0) (0,2) (0,2) Player 1 2 (1,0) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure. strategy Nash equilibria 2. Does the game have a mixed strategy equilibrium? If so, find one. Otherwise, provide an explanationWhich is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). B Right (2, 2) (1, 3) Left (3, 1) (0,0) Up A Down Which outcome is the Nash equilibrium in this game? (Up, Right) (Up, Left) (Down, Right) (Down, Left)