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- Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?Question 36 Consider the following normal form of a game. A D. (-3,-4) (-2,-5) (-1,0) (-4,-3) What is the maximin strategy of the row player? A O BConsider the following extensive form game between player 1 and player 2. T B (2, 2) L R R (3, 1) (0, 0) (5, 0) (0, 1) (a). Find the normal form representation of this game. (show the bimatrix) (b). Find all pure strategy NE. (c). Which of these equilibria are subgame perfect?
- 1. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,3a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to3. Find the dominant and dominated strategies in the following games (in case players have such strategies). Is there any dominant strategy equilibrium in any of these games? (a) Player 2 L R Player 1 U 5,5 3,6 D 6,3 4,4 (b) Player 2 V W X Y Z A 2,5 4,4| 5,5 | 0,4 | 1,5 B 5,3 3,3 4,3 | 2,2 | 1,0 Player 1 C 6,0 | 3,0 | 1,1| 1,1 |0,1 D 6,2 3,0 | 4,2 | 3,2 | 1,2 E 1,1 5,1| 4,2 | 1,0 | 0,2
- 3. Determine the Nash Equilibrium for the following normal form of the game. A) MARY B) UP DOWN PLAYER 1 HARLEY UP (10, 10) (4,8) LEFT (3,0) UP MIDDLE (1, 1) DOWN (0,1) DOWN (8,4) (5,5) PLAYER 2 CENTER RIGHT (2,1) (1,1) (4,2) (0,0) (5,0) (0,1)Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
- Question 28 What is the dominant strategy of the column player? 2 N 40,30 20,50 25,50 20, 20 1 P Q R S M 50, 20 15,30 25,30 0,20 0 45, 20 30, 40 35,50 40,5Question 5 Consider following extensive form game Keep Prices (8,2) Advertise Lower Prices (4,6) O Advertise; Lower Prices Firm 1 O Advertise; Keep Prices Firm 2 O Not Advertise; Keep Prices Not Advertise The subgame perfect Nash-equilibrium is O Not Advertise; Lower Prices Keep Prices (6,10) O Lower Prices (3,7) 5 pts5) Consider the following simultaneously move game. Player 1\Player 2 Top Middle Bottom Find Nash equilibrium. Left 2,2 1,3 3,1 Center 0,0 3,0 2,3 Right 1,3 1,0 2,2