1. mixed). P₁ $1 82 Consider the following symmetric game. Find all evolutionarily stable strategies (pure and/or P₂ $1 82 83 1,1 4,9 0,3 9,4 0,0 0,3
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- Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)In the following symmetric general sum game (2, 2) (0,0) (0,0) (0,0) (0,0) (2, 2) (0,0) (2,2) (0,0) (i) Find all pure Nash equilibria. (ii) Find all mixed Nash equilibria in which all probabilities are positive. (vi) Which of these are evolutionary stable strategies?Asap
- Q2 Consider the following game. (a) Find all pure-strategy Nash equilibria. (b) Find all mixed-strategy Nash equilibria. 2, 4 6, 0 5,1 1,9 A ВWith what probability does player 1 play Down in the mixed strategy Nash equilibrium? (Input your answer as a decimal to the nearest hundredth, for example: 0.14, 0.56, or 0.87). PLAYER 1 Up Down PLAYER 2 Left 97,95 47, 33 Right 8,43 68,91Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
- W X Y Z 47, 15| 39, 41 45, 53 12, 56 In equilibrium, what is the probability that player 1 will use the pure strategy X in this game?9 00 3 -2 -8 A = ( ) and B = 03 -5 -2 Let I be the bimatrix game whose payoffs are described by A for the row-player and B for the column- player. 1. Compute all mixed Nash equilibria of T. 9Find an equilibrium in the following game, with Nature moving first, with fixed probabilities as shown. (0,2) (2,2) B Q 2 (4,0)N N (6,0) .1 (0,0) (2,0) F .9 F B Q (6,2) N 2 1 -(4,2)
- 7. N [0.75] B A [0.25] 1 E F 6 2 J K J K 12 3 9. 6 6. 1 In equilibrium, what is the probability that player 1 will use the pure strategy E in this game?F G H 1 3 6 3 A 6. 8. 8 5 3 B 3 3 4 4. 9. C 5 3 a.) Find all pure-strategy Nash equilibria of the above game. b.) * Prove that there is a Nash equilibrium in which Player 2 chooses H, while Player 1 chooses A with probability 0.4 and chooses C with probability 0.6. 00 2,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 ()