Quantitative Analysis and Game Theory
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Quantitative Analysis (Show All Work)
#1
Solve the following Game:
Y1 Y2
X1 -5 -10
X2 12 8
X3 4 12
X4 -40 -5
#2
For the following two-person, zero-sum game, are there any dominated strategies? If so, eliminate any dominated strategy and find the value of the game.
Y1 Y2 Y3
X1 4 5 10
X2 3 4 2
X3 8 6 9
#3 Probability
A silver dollar is flipped twice. Calculate the probability of each of the following occurring:
a. a head on the first flip
b. a tail on the second flip given that the first toss was a head
c. two tails
d. a tail on the first and a head on the second
e. a tail on the first and a head on the second or a head on the first and a tail on the second
f. at least one head on two flips
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Solution Summary
The solution produces a game theory based on:
Quantitative Analysis (Show All Work)
#1
Solve the following Game:
Y1 Y2
X1 -5 -10
X2 12 8
X3 4 12
X4 -40 -5
#2
For the following two-person, zero-sum game, are there any dominated strategies? If so, eliminate any dominated strategy and find the value of the game.
Y1 Y2 Y3
X1 4 5 10
X2 3 4 2
X3 8 6 9
#3 Probability
A silver dollar is flipped twice. Calculate the probability of each of the following occurring:
a. a head on the first flip
b. a tail on the second flip given that the first toss was a head
c. two tails
d. a tail on the first and a head on the second
e. a tail on the first and a head on the second or a head on the first and a tail on the second
f. at least one head on two flips
Solution Preview
Quantitative Analysis (Show All Work)
#1
Solve the following Game:
Y1 Y2
X1 -5 -10
X2 12 8
X3 4 12
X4 -40 -5
#2
For the following two-person, zero-sum game, are there any dominated strategies? If so, eliminate any dominated strategy and find the value of the game.
Y1 Y2 Y3
X1 4 5 10
X2 3 4 2
X3 8 6 9
#3 Probability
A silver dollar is flipped twice. Calculate the probability of each of the following occurring:
a. a head on the first flip
b. a tail on the second flip given that the first toss was a head
c. two tails
d. a tail on the first and a head on the second
e. a tail on the first and a head on the second or a head on the first and a tail on the second
at least one head on two flips
EXPLANATION FOR #1 & #2
Game theory describes the situations involving conflict in which the payoff is affected by the actions and counter-actions of intelligent opponents. Two-person zero-sum games play a central role in the development of the theory of games. In order to develop the concepts, consider the following game in which player I has two choices from which to select, and player II has three alternatives for each choice of player I. The payoff matrix T is given below:
player II
j=1 j=2 j=3
player I i=1 4 1 3
i=2 2 3 4
______________________________________
The Payoff Matrix
In the payoff matrix, the two rows (i = 1, 2) represent the two possible strategies that player I can employ, and the three columns (j = 1, 2, 3) represent the three possible strategies that player II can employ. The payoff ...
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