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- Solve the Nash equilibrium for the following game (P1,P2) R T (2,4) (4, 6) (2,7) (3, 1) O (T,R) O (B,L) O (B,R) O (T,L)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 ()Find the mixed-strategy Nash equilibrium of the following normal-form game(Gibbons exercise 1.12) L R T 2,1 0,2 B 1,2 3,0
- Which of the following conditions correctly describes a Nash equilibrium when two firms are in the market? Multiple Choice n91s1. $2)2 (51. $2) for all s1 and 12(51, $2)212(51. 52) for all s2. aqls1, s2)22(s1, s2) for all s1 and a2(s1, 52) 2 n1ls1.52) for all s2. Rylsi. s2)2 als1. 52) for all s as1. 52)22(1. s2) for all sy and a2(s. s2)2 a1(s1, s2) for all s2With 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 68,91Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1. At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. For player 2, A stands for Accommodate and F stands for Fight. Player 1 Enter Player 2 A F A Stay out Player 2 F (16,30) (-6,18) In the Nash equilibrium of this game, player 2 earns Player 2 player 1 would play (0,40) (0,20) ✓an incentive to threaten F because, if player 1 believed him then so that player 2 would earn ✓. However, this threat is
- Keep Prices Advertise Lower Prices (4.6) Firm 1 Advertise; lower prices Not advertise; lower prices Advertise; keep prices Not advertise; keep prices Firm 2 Not Advertise Keep Prices (15,5) Consider the above extensive form game. The subgame perfect Nash-equilibrium is Lower Prices (6,10) (5,11)Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.In the following game, find the dominated strategies for each player and the reduced game and solve the pure equilibrium strategy. Also solve the mixed equilibrium strategy, if it doesn't exist, explain Y1 Y2 Y3 |(10,-10) (2,-2) X1 |(4,-4) (5,-5) X2 (3,-3) (4,-4) X3 (8,-8) (6,-6) (9,-9)
- 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)Consider the Normal Form Game characterized in the following figure: P1 \ P2 b1 b2 b3 a1 (1,2) (0,1) (0,3) a2 (3,-1) (1,1) (-1,0) a3 (2,2) (1,-1) (3,0) a4 (-5,1) (-1,0) (-3,-2) a5 (-3,3) (3,0) (2,4) What is the set of actions of player 1? O la 1, a2, a3, a4, a5) O (b1,b2, b3} O {a2, a3, a4) O (bl, b2}Can you help me with the question below? What is [are] the Nash Equilibrium [Equilibria] of this game? A) (10;10) and (20;20) B) (30;30) C) (10;20) and (20;10) D) (20;20) E) (30;30)