What is the dominant strategy of the row player? Column Row O Top O None O Bottom O Middle Top Middle Bottom Left (-5, -1) (1, -3) (0, 10) Center (2, 2) (1,2) (0, 0) Right (3, 3) (1, 1) (0, -10)
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- 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 B1. 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 3,3Player 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
- 3. 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 | 0,23. 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)Pay-offs (in terms of profit) for the two firms are give Firm2 startegies Firm1 Strategies C B W C [4, 4] [0, 5] [-1, 5] [5, 0] [2, 2] [-1, 1] W [5, -1] [1, -1] [0, 0] a)What is a dominant strategy for each player? b)What are the possible pure strategy Nash equilibrium/equilibria to the one-shot play of this game? c) Explain the likely out the game
- Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…
- 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 40,5c) Please find below Pricing options for firm A and B, along with individual payoffs (Firm A’s payoff/Firm B’s payoff)Firm BFirm APrice £2 Price £1Price £2 £10,000/£10,000 £5,000/£12,000Price £1 £12,000/£5,000 £6,000/£6,000Assume you are the pricing manager at Firm A;9i) What is your payoff for a ‘maximin’ strategy?ii) What is your payoff for a ‘maximax’ strategy? iii) Does a dominant strategy exist within this prisoners’ dilemma?Consider 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?