EBK MICROECONOMICS
2nd Edition
ISBN: 9780134458496
Author: List
Publisher: VST
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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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Consider the payoff matrix below which shows the cleaning strategies of two roommates, Patrick and Cameron.
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.
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