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Topic 4, HW 4, MAT 470, GCU
10.1 # 3:
For each game in this problem, plot the payoffs and use the plot to determine if the game is
a total conflict or partial conflict game.
a)
Rose
????
????
Colin
????
(2, -2)
(3, -3)
????
(1, -1)
(4, -4)
????
????
Colin
????
(2, 2)
(1, 4)
????
(4, 1)
(1, 1)
b)
Rose
c)
Pitcher
Batter
Fastball
Knuckleball
Guesses fastball
(0.400, -0.400)
(0.100, -0.100)
Guesses knuckleball
(0.300, -0.300)
(0.250, -0.250)
d)
Predator
Prey
Ambush
Pursue
Hide
(0.3, -0.3)
(0.4, -0.4)
Run
(0.5, -0.5)
(0.6, -0.6)
2
e)
Colin
Rose
????
????
????
(3, 5)
(0, 1)
????
(6, 2)
(-1, 4)
10.1 # 4:
Consider the following game, called the PrisoneràDilemma. The game goes as follows: We
assume that the police have arrested two suspects for a crime. Two prisoners have the
option to confess or not to confess to a crime they committed. The prosecutor has only
enough evidence to convict both criminals of a minor charge and is relying on obtaining a
confession. The minor offense carries a maximum sentence of only 1 year whereas the
crime committed nets a maximum of 20 years. The prisoners are questioned in different
interrogation rooms without the ability to communicate with one another. They are told
that if one of them confesses while the other remains silent, the one confessing individual
will go free, and the other will be arrested and charged with the crime for the 20-year
sentence. If both prisoners confess, then the reduced sentence will be only 5 years each. The
game table is as follows:
Prisoner 2
Prisoner 1
Confess
Not Confess
Confess
(-5, -5)
(0, -20)
Not Confess
(-20, 0)
(-1, -1)
a) Identify any dominant strategies for Prisoner 1.
b) Identify any dominant strategies for Prisoner 2.
c) Using the movement diagram, ?nd the Nash equilibrium.
d) Do you think that the Nash equilibrium is the best solution for both prisoners?
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10.2 # 2:
For problems a, c, e build a linear programming model for each playeràdecisions and
solve it both geometrically and algebraically. Assume the row player is maximizing his
payoffs which are shown in the matrices below
a)
Colin
Rose
????
????
????
10
10
????
5
0
c)
Pitcher
Batter
Fastball
Knuckleball
Guesses fastball
0.400
0.100
Guesses knuckleball
0.300
0.250
e) A predator has two strategies for catching a prey (ambush or pursuit). The prey has two
strategies for escaping (hide or run)
Predator
Prey
Ambush
Pursue
Run
0.20
0.40
Hide
0.80
0.60
4
10.4 # 3:
In the following problems, use the maximin and minimax method and the movement diagram to determine if any pure strategy solutions exist. Assume the row player is
maximizing his payoffs which are shown in the matrices below.
Pitcher
Batter
Fastball
Knuckleball
Guesses fastball
0.400
0.100
Guesses knuckleball
0.300
0.250
10.4 # 5:
A predator has two strategies for catching a prey (ambush or pursuit). The prey has two
strategies for escaping (hide or run). The payoff matrix entries, the chance of survivability,
allow the prey to maximize and the predator to minimize.
Predator
Prey
Ambush
Pursue
Run
0.20
0.40
Hide
0.80
0.60
5
10.6 # 2:
Use movement diagrams to ?nd all the stable outcomes in Problems 1 through 5. Then use
strategic moves (using Table 10.2 ) to determine if Rose can get a better outcome.
Colin
Rose
????
????
????
(1, 2)
(3, 1)
????
(2, 4)
(4, 3)

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