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    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

    © BrainMass Inc. brainmass.com October 9, 2019, 3:33 pm ad1c9bdddf
    https://brainmass.com/statistics/quantative-analysis-of-data/quantitative-analysis-game-theory-7141

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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
    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 ...

    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

    $2.19