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- Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 30, 30 16, -50 B -50, 16 50, 50 A. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. check all that apply (16, −50) (−50, 16) (30, 30) (50, 50) Which of these outcomes would you consider most likely? multiple choice (16, −50) (50, 50) (−50, 16) (30, 30) B. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter? multiple choice A or B What outcome do you think would occur as a result? multiple choice (−50, 16) (16, −50) (30, 30) (50, 50) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is…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 NoUse the following normal-form game to answer the following questions. a. For what values of x is strategy D (strictly) dominant for player 2? b. For what values of x is strategy B (strictly) dominant for player 1? c. For what values of x is (B, D) the only Nash equilibrium of the game?
- Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 50, 50 -110, 6 B 6, -110 26, 26 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.check all that apply (26,26) (50,50) (-110,6) (6,-110) Which of these outcomes would you consider most likely?multiple choice 1 (-110,6) (50,50) (6,-110) (26,26) b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?multiple choice 2 B A What outcome do you think would occur as a result?multiple choice 3 (26,26) (50,50) (-110,6) (6,-110) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move…The following payoff matrix represents a simultaneous-move game between two players: Kay and Jack. Each player has two choices: Black or White. The first number in each cell is the payoff to Kay, and the second number is the payoff to Jack. Jay Black White 50, 30, Black 50 30 Кay 45, 40, White 30 50 Refer to the scenario above. Which is true? a. This game has a dominant strategy equilibrium. b. This game has two dominant strategy equilibria. c. This game has two Nash equilibria. d. This game has one Nash equilibrium.conside the following game There are two companies that sell Haitian coffee.Each company currently makes $5 million in revenue They need to determine whether they should engage in a social media advertising campaign Advertising costs $2 million for each company If one company advertises and the other does not, then the one that advertises captures $3 million from the company that does not. If both companies advertise they gain nothing. Draw the payoff matrix. What is this games Nash equilibrium
- In a game of chicken, two drivers are heading towards each other on a collision course. The first one to swerve is considered the "chicken" and loses. What is the Nash equilibrium in this game? a) Both drivers swerve b) Neither driver swerves c) One driver swerves while the other doesn't d) It depends on the specificFind all of the Nash equilibrium of the following three player game. Player 1 chooses rows (a,b). Player 2 chooses columns (c,d). Player 3 chooses matrices (x.y). Player 3 receives the third listed payoff for cach outcome. 5,5,5 4,4,0 8,8,3 7,7,3 1,3,1 4,2,0 3,2,4 3,1,0 a by A) (b,d.x) and (a,d.y) B) (b.cy) OC) (b,d,x) D) (a,d,x) and (b,c.y) E) (b,c,x) OF) (a,d.x)Use the following normal-form game to answer the questions below. Player 1 (B.C) (B.D) (A.C) (A.D) Strategy A B a. Identify the one shot Nash equilibrium. 60, 60 30, 130 Yes Player Z D 130, 30 80, b. Suppose the players know this game will be repeated exactly three times, Can they achieve payoffs that are b shot Nash equilibrium?
- 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.Consider the following game where two players have to decide if they want to buy a movie ticket or a baseball ticket. They have the highest payoffs when they both buy tickets to the same activity, but must decide simultaneously what to buy without knowing what the other person will do. a. Does either player have a dominant strategy? b. How many equilibria does this game have? c. Is this an example of a prisoner’s dilemma? Explain. d. What will be the outcome if your friend buys their ticket first and you can observe their choice?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 Left Right (3, 1) (5,7) (4, 3) Center (1, 4) (2, 2) (3, 2) (6, 2) (4, 6) (5, 5) Up Middle Down Which of the following outcomes represents a Nash equilibrium in the game? (Up, Center) (Middle, Right) (Down, Left) (Down, Center)