Use the figure below to determine the dominant strategy for each player, if a dominant strategy exists. Player A Strategy 1 Strategy 2 10 11 Strategy 1 Player B 2 7 3 What is the dominant strategy for Player A? What is the dominant strategy for Player B? Strategy 2 (Click to select) (Click to select) 4 5

Use the figure below to determine the dominant strategy for each player, if a dominant strategy exists. Player A Strategy 1 Strategy 2 10 11 Strategy 1 Player B 2 7 3 What is the dominant strategy for Player A? What is the dominant strategy for Player B? Strategy 2 (Click to select) (Click to select) 4 5

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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6) The following is a static game D 2,2 0,3 D 3,0 1,1 a) Convert this game into dynamic form game b) Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. c) If you consider this game as dynamic then what kind of dynamic game is this.
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.
Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium (You must clearly label each answer in eCourses to receive any credit for your answers.) Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana 70 300 Inc. Strategy B 400 40 80 100 90 150 80 Strategy C
Q3 Consider the following three-player normal form game (Player 3 is the page player): Player 3 A в Player 2 Player 2 A в A B 1,2, 3 в 2,3,1 Player 1 A Player 1 A 2, 1, 3 3, 2, 1 3, 2, 1 1,2, 3 в 1,3, 2 3, 1,2 For each player, strategies are A and B. a) Find the pure strategy Nash equilibrium of the above game. Assume now that the above game is played sequentially, with Player 3 moving first, Player 1 moving second, and Player 2 moving third. b) Write down the game tree. c) For each player, list all the available pure strategies. d) Find the subgame perfect equilibrium outcome and compare it with the equilibrium outcome you found in subquestion a). Comment.
1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?
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.
12) What is a Nash equilibrium? Why do we generally think that Nash equilibria will be likely outcomes of games?
Consider a game where each player picks a number from 0 to 60. The guess that is closest to half of the average of the chosen numbers wins a prize. If several people are equally close, then they share the prize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30;(C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization.
8) Consider the following game: There are 10 players. Each player is asked to write a number between 0 and 100. The player whose choice is closest to half of the average is the winner. Describe the game and discuss what would you expect to be the average number if the game were played in class with your colleagues. Do you expect them to play the Nash equilibrium strategy? Explain.
The following is a static game: Convert this game into dynamic form game. Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. If you consider this game as dynamic then what kind of dynamic game is this.
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
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 No