Microeconomics (2nd Edition) (Pearson Series in Economics)
2nd Edition
ISBN: 9780134492049
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Question
Chapter 13, Problem 3P
(a)
To determine
Pay-off matrix for the game between Westley and Vizzini.
(b)
To determine
Strategies of Westley and Vizzini, if they are dominant or not.
(c)
To determine
Existence of Nash equilibrium in a pure-strategy game between Westley and Vizzini.
(d)
To determine
Value of a for which Westley has a dominant strategy.
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We consider the following three-player strategic form game, where Alice's strategies are U, C, and D, and Bob's strategies are L, M, and R, and Carol's strategies are A and B. Carol's strategy consists of choosing which table will be used for the payoffs, Table A or Table B.Table A is below, where for each cell the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff..
L
M
R
U
8,11,14
3,13,9
0,5,8
C
9,9,8
8,7,7
6,5,7
D
0,8,12
4,9,2
0,4,8
Table A
Table B is below, where again, for each cell, the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff..
L
M
R
U
14,1,0
13,2,11
1,3,2
C
0,0,2
7,2,3
14,3,2
D
7,12,11
12,12,0
2,11,2
Table B
This game may not have any Nash equilibrium in pure strategies, or it may have one or more equilibria.How many Nash equilibria does this game have?
Consider a game with two players A and B and two strategies X and Z. If both players play strategy X, A will earn $300 and B will earn $700. If both players play strategy Z, A will earn $1,000 and B will earn $600. If Player A plays strategy X and player B plays strategy Z, A will earn $200 and B will earn $300. If Player A plays strategy Z and player B plays strategy X, A will earn $500 and B will earn $400. Player B finds that:
a) strategy Z is a dominant strategy.
b) strategy X is a dominant strategy.
c) he has no dominant strategy.
d) strategy X is a dominated strategy.
e) strategy Z is a dominated strategy.
Consider a new card game between 2 players: Jim (player 1) and Kelly (player 2)
Jim is dealt two cards : 09 and 49. Kelly is also dealt two cards: 06 and 4. Now, each of the players will play 1 card both at the same time.
The payoff of Jim is 1 points if he plays a card of opposite color (red/black) than Kelly, and otherwise his payoff is 7 points.
The payoff of Kelly is 5 points if the difference of the already played card numbers is greater than 6, otherwise her payoff is 8 points.
1. Find the action sets of each player and the action profile of the game.
2. Represent the game in the Normal form.
3. Find the Best Responses for Jim.
4. Find the Best Responses for Kelly.
5. Find all the Nash Equilibriums of the game (if any).
Chapter 13 Solutions
Microeconomics (2nd Edition) (Pearson Series in Economics)
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