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- asapConsider 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}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?
- Based on the following game, what are the secure strategies for player 1 and player 2? Player 1 S1 and 12 S1 and t1 S2 and 12 S2 and 11 s1 S2 Player 2 tl 10,15 -10,7 t2 15,8 10,20GAME Z Player A B1 A1 7, 13 A2 3,8 Player B B2 15, 10 9,16 A3 5,8 4,7 In Game Z (see table above), assuming players move simultaneously. Which of the following is true? Player A has a dominant strategy Player B has a dominant strategy Both players have dominant strategies O Neither player has a dominant strategyLet G₁, G₂ and G3 be the following games. Colin A Rose B A (10,3) (7,5) B (6,6) (8.4) G₁ Rose Rose Colin A B A (4,4) (3,6) B (5,3) (2,7) G3 Colin A B A (5,8) (4,2) B (9,2) (3,5) G₂ Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution.
- Consider the following game: Player 1 T M B N R (1,2) (1,1) (3,4) (1,-1) L Player 2 (-1,2) (2, -1) (0,1) (4,4) S (3,2) (4,5) (5,4)) (6,1) Q (1,5) (1,2) (4,1) (1,4) a) Does player 1 (the row player) have any dominated strategies. If yes, list all such strategies b) Find all the Pareto Optimal strategy profiles in the game. c) Let 0= (1/2, 0,1/4,1/4). Find BR₂(0).GAME 5 Player B B1 B2 Player A A1 7,3 | 5, 10 A2 3, 8| 9, 6 In Game 5 above, O Neither player has a dominant strategy. O Player B has a dominant strategy. O Player A has a dominant strategy. O Both players have dominant strategies.Consider the Normal Form Game characterized in the following figure: P1 \ P2 A1 A2 A3 A4 Is the following statement True or False: Strategy (0,1,0,0) is Strictly Dominated for player 1? True B1 B2 B3 B4 (-1,1) (0,0) (1,-1) (2,0) (-2,-2) (2,7) (-1,-1) (-1,1) (5,7) (3,5) (0,0) (0,8) (0,3) (-1,-1) (10,2) (0,0) False
- (d) Consider a simultaneous-move game between two firms choosing to sell their product at either £6, £7 or £8. The actions and payoffs are given in the matrix below. Firm 2's Prices £6 £7 £8 Firm 1's prices £6 4, 5 3, 5 2, 1 £7 0,4 2, 1 3,0 £8 -1, 1 4, 3 0, 2 What are the Nash equilibria of this game? Game theory is often used by firms competing under an oligopoly as a means of determining their best strategy. Why is game theory a useful tool and which characteristics of an oligopoly make it particularly useful for firms competing in this market structure? One outcome of an oligopoly is that firms may have an incentive to collude. Explain some of the conditions that make collusion more likely to occur and how game theory can explain why collusive agreements often break down.8) Find the mixed strategy Nash equilibrium of the following normal form game. Player 2 T1 T2 T3 2, 3 3, 5 1, 1 Player 1 S2 1, 4 4, 3 0, 5 Player 1 attaches probability (S1, S2) = () and Player 2 attaches probability (T1, T2, T3) = ( ) Player 1 attaches probability (S1, S2) = (.) and Player 2 attaches probability (T1, T2, T3) = (qi, 42, 1 – q1 – 92) where q1 , and 0 < q2 S %3D Player 1 attaches probability (S1, S2) = (G,;) and Player 2 attaches probability (T1, T2, T1) = (qı.42, 1 – q1 – 42) where 0 < qi <, and q2 = 3. Player 1 attaches probability (S1, S) = (;, -) and player 2 attaches probability (T1, T2, T3) = (1.42, 1- q1- 42) where 0 s qı s and q2 =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)