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Decision Science - Game Theory

1. The Army is conducting war games in Europe. One simulated encounter is between the Blue and
Red Divisions. The Blue Division is on the offensive; the Red Division holds a defensive position.
The results of the war game are measured in terms of troop losses. The following payoff table shows
Red Division troop losses for each battle strategy available to each division:
Blue Division
Red Division Strategy
Strategy A B C
1 1,800 2,000 1,700
2 2,300 900 1,600
Determine the optimal strategies for both divisions and the number of troop losses the Red
Division can expect to suffer.

3. Mary Washington is the incumbent congresswoman for a district in New Mexico, and Franklin
Truman is her opponent in the upcoming election. Because Truman is seeking to unseat Washington,
he is on the offensive, and she hopes to minimize his gains in the polls. The following payoff table
shows the possible percentage point gains for Truman, given the political strategies available to each
politician:
Franklin Truman
Mary Washington Strategy
Strategy A B
1 7 3
2 6 10
a. Determine the optimal political strategy for each politician and the percentage gain in the polls
Franklin Truman can expect.
b. Solve this problem by using the computer.

5. Two major soft drink companies are located in the Southeast—the Cooler Cola Company and
Smoothie Soft Drinks, Inc. Cooler Cola is the market leader, and Smoothie has developed several
marketing strategies to gain a larger percentage of the market now belonging to Cooler Cola. The following payoff table shows the gains for Smoothie and the losses for Cooler, given
the strategies of each company:
Smoothie
Cooler Cola Strategy
Strategy A B C
1 10 9 3
2 4 7 5
3 6 8
Determine the mixed strategy for each company and the expected market share gains for
Smoothie and losses for Cooler Cola.

Solution Preview

See the attached file.

1. The Army is conducting war games in Europe. One simulated encounter is between the Blue and Red Divisions. The Blue Division is on the offensive; the Red Division holds a defensive position. The results of the war game are measured in terms of troop losses. The following payoff table shows Red Division troop losses for each battle strategy available to each division:
Blue Division
Red Division Strategy
Strategy A B C
1 1,800 2,000 1,700
2 2,300 900 1,600
Determine the optimal strategies for both divisions and the number of troop losses the Red
Division can expect to suffer.

This is a two person zero sum game where Red Division is the one that is trying to minimize its losses.

Strategy C for Red Division dominates both strategy A as its payoff for both strategies of Blue division is better than that of A. (1700 is less than 1800 and 1600 is less than 2300). Hence, strategy A can be eliminated from the game. The payoff table then can be given as;
B C
1 2000 1700
2 900 1600

Now, between strategy 1 and 2, Strategy 1 dominates strategy 2. Hence, Blue Division would choose strategy 1 as its optimal strategy.
Hence, the optimal strategy for Red division is Strategy C and the expected troop losses the Red division can expect to suffer are 1700.

3. Mary Washington is the incumbent congresswoman for a district in New Mexico, and Franklin Truman is her opponent in the upcoming election. Because Truman is seeking to unseat Washington, he is on the ...

Solution Summary

The solution discusses decision science, specifically the game theory.

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