Explore BrainMass

Explore BrainMass

    Two player game, Decision alternatives

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    1. Here is the description of a two player game. Player A selects a, b, or c. Player B selects i, ii, or iii.

    Player B
    i ii iii
    a 5 7 2
    Player A b 4 8 5
    c 6 4 3

    Payoffs are to Player A. This is a zero sum game.

    a.                   Indicate any dominated strategies and restate the game appropriately
    b.                  Determine the optimal strategies for the players
    c.                   What is the value of the game?

    ---------

    2. You are the general manager of Keystone Chemicals Houston plant. Following a recent visit by corporate officials, you have received a memo directing you to upgrade plant security. The memo requires you upgrade protection in three areas:
    1.      Protection against forced entry and theft/destruction (F)
    2.      Protection against entry by subterfuge and theft (S)
    3.      Protection of trade secrets and proprietary information (T)
    The memo also cautions that any measures taken must be carefully evaluated for their cost-effectiveness (C).

    After careful research, you have determined that there are three responses that could satisfactorily address the mandate you have received. Each addresses the three areas differently and each has a different cost. The three responses are:
    1.      Improve the electronic surveillance at the plant (El)
    2.      Hire a security service for foot and K-9 patrols. (Out)
    3.      Improve in-house security staffing (personnel levels and training). (In)

    You have rated the alternative responses in terms of how well they address the areas of concern and their cost. You have assigned the weights (suggesting relative strength of concern) to the areas and the cost. The table summarizing what you have done follows.

    Weights -> 3 3 4 6
    C F S T
    El 7 2 8 5
    Out 6 7 5 3
    In 5 6 7 5

    a. Which choice is indicated by his ratings?
    b. Is an alternative dominated? why?
    c. What is the weight for S that will produce indifference between the two top ranked choices? Write the algebraic expression and solve it.

    ----------

    4. Ace Venture Capital (AVC) has a million dollars to invest. It is considering two proposals. One proposal is to invest with the operator of retail shoe stores. The investment will produce a majority stake in a corporation that owns three retail outlets. These will be managed by the entrepreneur who is also investing $1 million in the corporation. The other proposal is to invest in a software company that provides learning space on the internet for Universities that provide on-line education. After evaluating both business plans the projected performance of each alternative investment (% returns to AVC) is seen to depend on the state of the economy over the next 5 years. This information is summarized in the following table.

    Strong Economic Growth Modest Economic Growth
    Shoes 17% 13%
    Software 25% 8%

    Taking the position of AVC,
    a. If you are uncertain about the future state of the economy, which alternative should be chosen?
    b. What probability of Strong Economic Growth makes you indifferent between the investments?
    c. Stated as a percentage, what would you be willing to pay for perfect information about the future growth

    © BrainMass Inc. brainmass.com October 2, 2022, 4:07 pm ad1c9bdddf
    https://brainmass.com/business/entrepreneurial-issues/two-player-game-decision-alternatives-14807

    Attachments

    SOLUTION This solution is FREE courtesy of BrainMass!

    See attached files (either of them)

    1. Here is the description of a two player game. Player A selects a, b, or c. Player B selects i, ii, or iii.

    Player B
    i ii iii
    a 5 7 2
    Player A b 4 8 5
    c 6 4 3

    Payoffs are to Player A. This is a zero sum game.

    a. Indicate any dominated strategies and restate the game appropriately
    b. Determine the optimal strategies for the players
    c. What is the value of the game?

    2. You are the general manager of Keystone Chemicals Houston plant. Following a recent visit by corporate officials, you have received a memo directing you to upgrade plant security. The memo requires you upgrade protection in three areas:
    1. Protection against forced entry and theft/destruction (F)
    2. Protection against entry by subterfuge and theft (S)
    3. Protection of trade secrets and proprietary information (T)
    The memo also cautions that any measures taken must be carefully evaluated for their cost-effectiveness (C).

    After careful research, you have determined that there are three responses that could satisfactorily address the mandate you have received. Each addresses the three areas differently and each has a different cost. The three responses are:
    1. Improve the electronic surveillance at the plant (El)
    2. Hire a security service for foot and K-9 patrols. (Out)
    3. Improve in-house security staffing (personnel levels and training). (In)

    You have rated the alternative responses in terms of how well they address the areas of concern and their cost. You have assigned the weights (suggesting relative strength of concern) to the areas and the cost. The table summarizing what you have done follows.

    Weights -> 3 3 4 6
    C F S T
    El 7 2 8 5
    Out 6 7 5 3
    In 5 6 7 5

    a. Which choice is indicated by his ratings?
    b. Is an alternative dominated? why?
    c. What is the weight for S that will produce indifference between the two top ranked choices? Write the algebraic expression and solve it.

    1. Here is the description of a two player game. Player A selects a, b, or c. Player B selects i, ii, or iii.

    Player B
    i ii iii
    a 5 7 2
    Player A b 4 8 5
    c 6 4 3

    Payoffs are to Player A. This is a zero sum game.

    a. Indicate any dominated strategies and restate the game appropriately
    b. Determine the optimal strategies for the players
    c. What is the value of the game?

    a. Indicate any dominated strategies and restate the game appropriately
    If we observe ii and iii

    ii iii
    7 > 2
    8 > 5
    4 > 3

    Thus player B will always choose iii over ii as it would mean smaller payoff to A
    Thus ii is dominated strategy

    Thus the game can be reststed thus

    Player B
    i iii
    a 5 2
    Player A b 4 5
    c 6 3

    Now if we observe rows a and c

    a 5 2
    < <
    c 6 3

    Thus Player A will always choose c over a as it will give him higher payoff
    Thus a is dominated strategy

    Thus we can restate the game thus

    Player B
    i iii
    Player A b 4 5
    c 6 3

    b. Determine the optimal strategies for the players

    Player B Row minimum
    i iii
    Player A b 4 5 4
    c 6 3 3
    Column maximum 6 5
    Minimax= 5 = Minimum of (6,5)
    Maximin= 4 = Maximum of (4,3)

    There is no optimal strategy since Minimax is not equal to maximin
    There is no saddle point

    c. What is the value of the game?

    Maximin ≤ Value of the game ≤ Minimax
    4 ≤ Value of the game ≤ 5

    2. You are the general manager of Keystone Chemicals Houston plant. Following a recent visit by corporate officials, you have received a memo directing you to upgrade plant security. The memo requires you upgrade protection in three areas:
    1. Protection against forced entry and theft/destruction (F)
    2. Protection against entry by subterfuge and theft (S)
    3. Protection of trade secrets and proprietary information (T)
    The memo also cautions that any measures taken must be carefully evaluated for their cost-effectiveness (C).

    After careful research, you have determined that there are three responses that could satisfactorily address the mandate you have received. Each addresses the three areas differently and each has a different cost. The three responses are:
    1. Improve the electronic surveillance at the plant (El)
    2. Hire a security service for foot and K-9 patrols. (Out)
    3. Improve in-house security staffing (personnel levels and training). (In)

    You have rated the alternative responses in terms of how well they address the areas of concern and their cost. You have assigned the weights (suggesting relative strength of concern) to the areas and the cost. The table summarizing what you have done follows.

    Weights -> 3 3 4 6
    C F S T
    El 7 2 8 5
    Out 6 7 5 3
    In 5 6 7 5

    a. Which choice is indicated by his ratings?

    Weights -> 3 3 4 6 Weighted total
    C F S T
    El 7 2 8 5 89 =3*7+3*2+4*8+6*5
    Out 6 7 5 3 77 =3*6+3*7+4*5+6*3
    In 5 6 7 5 91 =3*5+3*6+4*7+6*5

    Therefore choose In (Improve in-house security staffing (personnel levels and training). (In))
    as it gives the maximum value of 91

    b. Is an alternative dominated? why?

    No alternative is dominated
    No row is greater than any other row for all the entries
    (maximum are highlighted)

    C F S T
    El 7 2 8 5
    Out 6 7 5 3
    In 5 6 7 5

    c. What is the weight for S that will produce indifference between the two top ranked choices? Write the algebraic expression and solve it.

    The two top ranked choices are EI and In

    Weights -> 3 3 4 6
    C F S T
    El 7 2 8 5 89 =3*7+3*2+4*8+6*5
    Out 6 7 5 3 77 =3*6+3*7+4*5+6*3
    In 5 6 7 5 91 =3*5+3*6+4*7+6*5

    Let the weight for S be x

    weighted total for EI= =3*7+3*2+x*8+6*5= 57 +8x
    weighted total for In= =3*5+3*6+x*7+6*5= 63 +7x

    Equating the two
    57 +8x = 63 +7x

    or x= 6

    the weight for S that will produce indifference between the two top ranked choices= 6

    Let us see whether this is the case

    Weights -> 3 3 6 6
    C F S T
    El 7 2 8 5 105 =3*7+3*2+6*8+6*5
    Out 6 7 5 3 87 =3*6+3*7+6*5+6*3
    In 5 6 7 5 105 =3*5+3*6+6*7+6*5

    This is indeed the case

    4. Ace Venture Capital (AVC) has a million dollars to invest. It is considering two proposals. One proposal is to invest with the operator of retail shoe stores. The investment will produce a majority stake in a corporation that owns three retail outlets. These will be managed by the entrepreneur who is also investing $1 million in the corporation. The other proposal is to invest in a software company that provides learning space on the internet for Universities that provide on-line education. After evaluating both business plans the projected performance of each alternative investment (% returns to AVC) is seen to depend on the state of the economy over the next 5 years. This information is summarized in the following table.

    Strong Economic Growth Modest Economic Growth
    Shoes 17% 13%
    Software 25% 8%

    Taking the position of AVC,
    a. If you are uncertain about the future state of the economy, which alternative should be chosen?

    Strong Economic Growth Modest Economic Growth Row minimum
    Shoes 17% 13% 13%
    Software 25% 8% 8%
    Column maximum 25% 13%
    Minimax= 13% = Minimum of (25%,13%)
    Maxmin= 13% = Maximum of (13%,8%)

    Thus if one is uncertain about the future state of economy he should choose Shoes
    as a minimum of 13% return is assured

    b. What probability of Strong Economic Growth makes you indifferent between the investments?
    probability p 1-p
    Strong Economic Growth Modest Economic Growth
    Shoes 17% 13%
    Software 25% 8%

    Let the probability of strong economic growth be p
    Therefore the probability of modest economic growth is ( 1- p)

    Return on investing in shoes= p(17%) + (1-p)(13%)= p(4%) + 13 %
    Return on investing in software= p(25%) + (1-p)(8%)= p(17%) + 8 %

    Equating the two
    p(4%) + 13 % = p(17%) + 8 %
    or p(13%)= 5%
    0r p= 38.46% =5%/13%

    Thus the probability of Strong Economic Growth to makes you indifferent between the investments= 38.46%

    We can see that such is the case
    Multiply the probability by the growth
    p 1-p
    probability 38.46% 61.54%
    Strong Economic Growth Modest Economic Growth
    Shoes 17% 13% 14.54% =38.46%*17.%+61.54%*13.%
    Software 25% 8% 14.54% =38.46%*25.%+61.54%*8.%

    Stated as a percentage, what would you be willing to pay for perfect information about the future growth

    If we have the perfect information

    probability decision return probability X return
    Strong Economic Growth 38.46% Software 25% 9.62% =38.46%*25.%
    Modest Economic Growth 61.54% Shoes 13% 8.00% =61.54%*13.%
    Total= 17.62%

    difference between the returns when perfect information is there and where there is no information
    3.08% =17.62%-14.54%

    Thus the maximum amount that can be paid for perfect information = 3.08% Answer

    4. Ace Venture Capital (AVC) has a million dollars to invest. It is considering two proposals. One proposal is to invest with the operator of retail shoe stores. The investment will produce a majority stake in a corporation that owns three retail outlets. These will be managed by the entrepreneur who is also investing $1 million in the corporation. The other proposal is to invest in a software company that provides learning space on the internet for Universities that provide on-line education. After evaluating both business plans the projected performance of each alternative investment (% returns to AVC) is seen to depend on the state of the economy over the next 5 years. This information is summarized in the following table.

    Strong Economic Growth Modest Economic Growth
    Shoes 17% 13%
    Software 25% 8%

    Taking the position of AVC,
    a. If you are uncertain about the future state of the economy, which alternative should be chosen?
    b. What probability of Strong Economic Growth makes you indifferent between the investments?
    Stated as a percentage, what would you be willing to pay for perfect information about the future growth

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 2, 2022, 4:07 pm ad1c9bdddf>
    https://brainmass.com/business/entrepreneurial-issues/two-player-game-decision-alternatives-14807

    Attachments

    ADVERTISEMENT