Pay-offs (in terms of profit) for the two firms are giveFirm2 startegiesFirm1 StrategiesC BWC[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 Nashequilibrium/equilibria to the one-shot play of this game?c) Explain the likely out the game

Dominant strategy in a game for any player is that strategy which has relatively better payoffs for…

Answered: Pay-offs (in terms of profit) for the…

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5PA

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Similar questions

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
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.
Find the unique Nash equilibrium of a game with the following payoff matrix: Player 2 2 4 1 (6, 7) (13, 8) (9, 9) Player 1 3 (4, 4) (7, 7) (7, 6) (7, 7) (11, 11) (7, 13) О a. (3, 2) O b. (5, 4) О с. (11, 11) O d. (1, 6) O e. There is no unique Nash equilibrium.
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)
1\2 L 1,-1 | 5,0 | 0,0 0,5 4,4 0,0 0,0 3,3 M R C 0,0 В 1. Find all set of rationalizable strategies (Hint: We are allowed to eliminate a pure strategy, if it is strictly dominated by a mixed strategy). 2. Find all set of pure strategy Nash equilibria. 3. Is there a dominant strategy equilibrium for this game?
Question 5 Consider the following Extended Form Game: A' (1,1) A P2 B' O [(B, B')} (2,3) O ((B.(B',A')). (B.(B¹, B'))) P1 A' What is the set of Nash Equilibria? O {(B.(A', B)), (B,(B', B'))) (4,5) B O ((B.(A'A')). (B.(A, B')). (B,(B,A')), (B,(B', B'))} P2 B' (6,7)
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 | 0,2
2. Consider the two-by-two bimatrix game listed below: Left Right (2,-2) (1,-1) Up Down (3,-3) (-1,1) where the player "Row" chooses the action "up" or "down" and the player "Column" chooses the action "left" or "right". Describe a mixed strategy Nash Equilibrium for this game.
(6) Find all the Nash equilibria and subgame perfect equilibria of the games in Figures 1 and 2 on the next page.
3) Consider the following two extensive form games and answer the following questions. How many subgames present in the following games? Find all pure strategies SPNE. Find all pure strategies NE of these games. Game A Game B u (5,3) u (0,2) 2 2 L L (-5,4) d (0,0) 1 1 1 (1,-5) (-10,-10) u R (2,3) A M 2 R 2 r d 1 (8,1) B (2,0) (2,2)
Consider the following simultaneous game: Player 1 U D Player 2 L 30,10 -10, 20 R 10, 20 5,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.
Consider the following two player extensive form game. メ (2,5) (4,) (3,5) a. Find the induced normal form of the given extensive form game using the pure strategies of the players. Find out all the possible Nash Equilibrium of this game. b. From the Nash Equilibrium you are getting in part a., which one is subgame perfect Nash Equilibrium? Explain with appropriate reasons. c. Explain why the NE in part b. is credible. (Use maximum 3 sentences):

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