Finally... for each of the following state the dominant strategies for each game and state the Nash Equilibrium point 9) Option Option Option D E F Option 16, 0 14, 2 17, 1 A Option 13, 0 9, 2 15, 1 Option 15, 0 10, 2 1, 1 C Dominant Strategies? Nash Equilibrium Point? The pay-off is highest at...
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- 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?Japan's Elpida Memory entered court management and was acquired by Micron. The media reportedthat it was the result of the semiconductor chicken game.■Question (a) Where is the Nash Equilibrium?■Question (b) What is the mixed-strategy equilibrium? – find out x and y■Question (c) What is the probability of a chicken game?Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.
- Find all Nash equilibria of the following two-player game. Provide necessary computation. L M R A 0,0 в (2,—1| 0,0 C -2,1 | 2, –1 0,0 -2,1 | 2, –1 -2, 12. Provide the normal-form expression to the extensive-form game below, and find all pure-strategy Nash equilibria there. Find the subgame-perfect Nash equilibrium then. A B X E Y B A B F t G F G BF B D A 0 3. Find the subgame perfect Nash equilibria (may or may not be unique) in the game below. A B 100 30 F 60 9 5 B 3 5 12 10 60 10 80 10 180 60 200 40Consider 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.
- Team 2 plays A Team 2 plays B Team 1 plays A 2, 1 0,0 Team 1 plays B 0,0 1, 2 Consider the game above. Which of the following is a Nash Equilibrium of the game? O Team 1 plays A two thirds of the time and plays the rest of the time, while team 2 plays A two thirds of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A one quarter of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A three quarters of the time and plays B the rest of the time. O None of the other answers are correct. Team 1 plays A two thirds of the time and plays B the rest of the time, while team 2 plays A one third of the time and plays B the rest of the time.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.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.)
- rock 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.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 ofConsider the following game. Which one of the following statements is TRUE? 1. There are 8 subgames for this extensive-form game. 2. There are 8 proper subgames for this extensive-form game. 3. There is no Subgame Nash Equilibrium for this game. 4. There exists some Subgame Nash Equilibrium that gives the payoff 7 to Player 1 and 3 to Player 2.