Microeconomics (13th Edition)
13th Edition
ISBN: 9780134744476
Author: Michael Parkin
Publisher: PEARSON
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Chapter 15, Problem 17APA
To determine
Identify the equilibrium of the repeated game.
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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.
1. With nash equilibrium, do you always choose the optimal strategy?
2. Can a game have more than one nash equilibrium?
Please answer all parts.
Two construction companies EdilA and EdilB take part in a race contract to build a school. Both can bid 1000, 2000 or 3000. The winner (the lowest offer) builds the school and pays 900 of costs.
1. When both bid the same amount, EdilA wins the contract. Find the Nash equilibrium.
2. Assume instead that when both bid the same, neither gets the contract, and furthermore suffer a penalty of 10. Find the Nash equilibrium.
3. Assume instead that when both bid the same, each builds half the school (but sustains 600 of costs, thus more than half). Find the Nash equilibrium.
4. Under the hypothesis of point 2 assume that EdilB can observe the offer made by EdilA before it makes its offer, and that EdilA anticipates that. Find the Nash equilibrium by backward induction of this sequential game.
Chapter 15 Solutions
Microeconomics (13th Edition)
Ch. 15.1 - Prob. 1RQCh. 15.1 - Prob. 2RQCh. 15.1 - Prob. 3RQCh. 15.1 - Prob. 4RQCh. 15.2 - Prob. 1RQCh. 15.2 - Prob. 2RQCh. 15.2 - Prob. 3RQCh. 15.2 - Prob. 4RQCh. 15.2 - Prob. 5RQCh. 15.2 - Prob. 6RQ
Ch. 15.3 - Prob. 1RQCh. 15.3 - Prob. 2RQCh. 15.4 - Prob. 1RQCh. 15.4 - Prob. 2RQCh. 15.4 - Prob. 3RQCh. 15.4 - Prob. 4RQCh. 15.4 - Prob. 5RQCh. 15 - Prob. 1SPACh. 15 - Prob. 2SPACh. 15 - Prob. 3SPACh. 15 - Prob. 4SPACh. 15 - Prob. 5SPACh. 15 - Prob. 6SPACh. 15 - Prob. 7SPACh. 15 - Prob. 8SPACh. 15 - Prob. 9APACh. 15 - Prob. 10APACh. 15 - Prob. 11APACh. 15 - Prob. 12APACh. 15 - Prob. 13APACh. 15 - Prob. 14APACh. 15 - Prob. 15APACh. 15 - Prob. 16APACh. 15 - Prob. 17APACh. 15 - Prob. 18APACh. 15 - Prob. 19APACh. 15 - Prob. 20APACh. 15 - Prob. 21APACh. 15 - Prob. 22APACh. 15 - Prob. 23APA
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- 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…arrow_forwardSam and Sarah are thinking about getting married. However if either of them cheats on the other, they would get a payoff of 10, while the other person gets zero. If neither cheat, they stay with each other and get a payoff of 7 each and if both cheat, the relationship falls apart and each get a payoff of 1. What is the Nash equilibrium of this game? a. Cheat, Cheat b. Not cheat, Not cheat Sam cheats, Sarah doesn't Sarah cheats, Sam doesn'tarrow_forwardWhat is the Nash Equilibrium in a game?A. A situation where all players cooperate for maximum gainB. A situation where no player can improve their outcome by changing their strategy unilaterallyC. A situation where players always choose the same strategyD. A situation where players randomly select strategiesarrow_forward
- 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.arrow_forwardone two X, 14 three four Firm B Low Firm A Sell High 6, Y Buy Low Let X = 9, Y = 15 and Z=10. This game has 10, Z Firm B High 8,8 Nash equilibrium.arrow_forwardUse 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 Noarrow_forward
- The next three questions pertain to the following normal-form game played by Pepsi and Coke: Coke Pepsi → | Advertise Don't 3.3 0,5 Advertise 5.0 Don't 4,4 7. Write in the blank Coke's best response to Pepsi, if Pepsi Advertises, 8. If the firms could collude, what pair of actions would they try and agre0 on (write "Advertise" or "Dont" on the line)? Pepsi: Coke: 9. What are the Nash equilibrium strategies of the firms? Coke: Pepsi:arrow_forwardTucker and Eddie are playing the following game. Tucker can choose A or B and Eddie can choose C or D. The first payoff is for Tucker, the second for Eddie. Eddie Tucker C D A 3, 2 4, 3 B 4, 5 3, 4 Identify the Nash equilibrium(s) in this game. What rational game theoretic advice would you offer Tucker and Eddie on how to play this game? If Tucker and Eddie follow your advice, what payoff should each expect? Show your work.arrow_forwardHow do we solve a Sequential-move game?arrow_forward
- Problem Consider the following finitely repeated date game. Write down a subgame perfect equilibrium. You can do this using informal descriptions of the strategies. Iya Froyo Iva Is Frou Froyo 0,0 6,1 1,5 0,0arrow_forwardWhat is the nash equilibrium of the game "sticks"?arrow_forwardGame theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 ہے A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.arrow_forward
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