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Consider the following game, where M > 0: The matrix payoff is shown below Gill Left Right James Accept 0, 0 2, −2 Reject ?, −? 1, −1 a) Do players have a dominant strategy? (b) What is the Nash equilibrium (or equilibria)? (c) Are there any values of M such there is no Nash equilibrium in pure strategy? ( d) Find the mixed strategies Nash equilibrium?
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- Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.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…(b) ROWENA up Answer 1: up Answer 2: In this simultaneous move game, the iterated dominance equilibrium is (Rowena's . Colin's left left Answer 3: ). This game has two Nash equilibria one of which is the iterated dominance equilibrium. The other Nash equilibrium, which is not the IDE, is (Rowena's down Colin's right down Up Down Answer 4: Left right 0,0 0,0 COLIN Right 0,0 1,1
- 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 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 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats 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. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 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 they agree upon, if any? a) Both…Use the following normal-form game to answer the questions below. Player 2 Strategy C D Player 1 A 50, 50 120, 25 B 25, 120 55, 55 a. Identify the one-shot Nash equilibrium.multiple choice 1 (B,C) (B,D) (A,C) (A,D) b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium?multiple choice 2 No Yes c. Suppose this game is infinitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium?multiple choice 3 No Yes d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is θ. If θ is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?multiple choice 4 Yes No2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.
- This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). B Right (2, 2) (1, 3) Left (3, 1) (0,0) Up A Down Which outcome is the Nash equilibrium in this game? (Up, Right) (Up, Left) (Down, Right) (Down, Left)Suppose that Green Giant and Red Rover are two companies competing in the canned vegetable market. Each is contemplating an aggressive new ad campaign. The payoffs of each decision are listed below, where Green Giant is player 1. Green/Red Ad Campaign No Ad Campaign |Ad Campaign |1 million, 1 million zero, 3 million No Ad Campaign 3 million, zero 2 million, 2 million What is the Nash equilibrium of the game? a. (advertise, don't advertise) b. (advertise, advertise) c. (don't advertise, don't advertise) d. (don't advertise, advertise)Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)
- Which is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)In the game presented in Table, what are the Nash equilibrium strategies for players A and B?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 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 V
