Consider the following game A 1.0 2.0 p.0 3.3 3.4 0,2 2.4 5. 2 How many Nash equilibria in pure strategies does this game have? OA0 OB1 OC2 O D.3 O E. More than 3
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- Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.Peter X O a. 3 O b. 2 O c. more than 3 O d. 1 O e. none Y Z R 9,6 6,6 9,7 How many (pure strategy) Nash equilibria does this game have? Sarah S 4,4 7,6 1,5 T 6,-3 2,2 6,72. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.
- The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofrock paper scissors rock 0. -3 0. раper scissors -1 -1 3. 0. (a) Show that xT= (,) and yT= (,) together are not a Nash equilibrium 3' 3 3131 for this modified game.L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?
- Consider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium OHawk, Dove ODove, Hawk O Hawk, Hawk O Hawk, Hawk3. Nash Equilibria Consider the following (normal-form) game. Compute a Nash Equilibrium of this game. U C D L | M R 5,0 1,3 4,0 2,4 1,4 3,5 0,1 1,0 5,0Consider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium O Hawk, Dove O Dove, Hawk O Hawk, Hawk O Hawk, Hawk
- on Mary, UE, BD UF, AC DF, BC UF, BD DE, AC DE, BC Nancy U D Nancy -5,4 Mary -0,2 -6,2 -2.6 Which of the following answers is a subgame perfect Nash equilibrium in this game? Check all that apply. (Answers below are formatted as Mary's strategy, Nancy's strategy.)GAME 5 Player B B2 B1 Player A A1 7, 3 5, 10 A2 3, 8 9, 6 In Game 5 above, O there are no Nash equilibria in pure strategies. Player A choosing A1 and Player B choosing B2 is a Nash equilibrium. O Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. O Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?