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parameter x =5
List all pure strategy Nash equilibria.
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- Consider the following strategic game with 2 players: P1 AND P2 E F G H A 10,30 0,50 5,5 40,20 B 40,10 10,10 8,20 30,5 C 15,5 10,30 5,20 25,20 D 20,3 20,8 6,6 20,0 (a) Specify the strategies for P1 and P2, respectively. Eliminate all strictlydominated strategies, and FIND the reduced game until you can reduce the game nofurther.(b) Find all the Nash equilibria for the reduced game, including the mixed-strategy onesClaim: The game in the table below is a strategic situation. Enter 111 for YES, 222 for NO and 999 for UNCERTAIN Firm A Left Straight Right Firm B Up 4,5 4,8 4,12 Middle 8,5 8,8 8,12 Down 9,5 9,8 9,12Suppose 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)
- Suppose there is a second price sealed bid auction in which the players have the following values: v1=15, v2=4, v3=6, v4=8, v5=10, v6=6. In the symmetric equilibrium, what bid will bidder 4 submit? a. 10 b. 15 c. 4 d. 8Refer to the accompanying game. Firm A Firm B Low Price High Price Low Price (10,9) (15,8) High Price (−10,7) (11,11) What are the secure strategies for firm A and firm B, respectively?Normal-Form GameFind all Nash equilibria of the following two-player game. Provide necessary computation.
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.What is the secure strategy for player B in the game presented in TableA game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
- Consider the game in the table below. Is the Nash Equilibrium efficient? Enter 111 for YES and 222 for NO. firm a left right firm b up 9,5 10,6 down 6,10 7,9Consider the following game 1\2 Y Z A 10,2 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (1/3,2/3) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, Player 2 should respond by playing ____would it be -3? if not, how do i find it? game theory