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Two player game, Decision alternatives

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
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


Solution Summary

Answers questions on two player game, decisions.