Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (2nd Edition)
2nd Edition
ISBN: 9780134641904
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Question
Chapter 18, Problem 6P
(a)
To determine
Game tree for the extensive-form game between Michael and Sollozzo.
(b)
To determine
Michael will not meet Sollozzo in the given game.
(c)
To determine
Sequence of the game when the Bocchichhio family gets involved.
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Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 6 and Deborah will receive a payoff of 5.
Deborah
Left
Right
Carlos
Left
8, 4
4, 5
Right
5, 4
6, 5
The only dominant strategy in this game is for to choose .
The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses .
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 one-time game involving a penalty kick in football/soccer. There are two players: kicker and
goalkeeper. The kicker has two possible actions: kick left or right. The goalkeeper also has two possible
actions: guess left or right. The kicker and goalkeeper move simultaneously. If the kicker and goalkeeper
choose the same direction, the goalkeeper "wins" and the payoffs are (0,1). If the kicker and goalkeeper
choose different directions, the kicker wins and the payoffs are (1,0).
(a) Is there a pure strategy equilibrium in this game? Explain.
(b) Derive and explain the mixed strategy equilibrium for this game.
Chapter 18 Solutions
Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (2nd Edition)
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