# Payoff Table and Optimal Strategy

The president of a large oil company must decide how to invest the company's $10 million of excess profit. He could invest the entire sum in solar energy research, or he could use the money to research better ways of processing coal so that it will burn more cleanly. His only other option is to put half of this R&D money into solar research and half into coal research. The president estimates 1500% return on investment if the solar research is successful and 800% return on investment if the coal research is successful.

a. Construct a payoff table for the president's R&D investment problem.

b. What decision should the president make based on:

1. Maximin criterion

2. Maximax criterion

3. Laplace criterion.

4. Minimax regret criterion.

c. If the president estimates that the probability of the solar research being successful is 0.4 and the probability of successful research on coal is 0.7, and if the president is an EMV er, what is his optimal strategy?

d. Calculate (EVPI) using:

1. EPC and EMV.

2. EOL.

https://brainmass.com/math/probability/payoff-table-and-optimal-strategy-516592

#### Solution Preview

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a. The payoff table. The scenarios (or choices) are: choosing solar only (S), choosing coal only (C) and choosing half solar and

half coal (S&C). The possible scenarios are according to whether solar and/or coal are successful: Solar successful denoted +S,

coal successful.ll +C, solar failure -S, coal failure -C. The table is

...

where values are in millions. Note that investing $10 millions in successful solar gives a payoff of 1500 %, that is $15000

millions. Similarly for coal.

b.

Maximin criterion (maximize the minimum payoff for each choice). The minimum payoff in any of the three choices is zero,

so any of the three, S,C or S&C, fulfills the Maximin criterion.

Maximax criterion (maximize the maximum payoff for each ...

#### Solution Summary

We construct a payoff table to study the different possible scenarios in decision making. We decide the best strategy based on different criterion: maximin, maximax, Laplace, minimax.

Later, given probabilities of success for each choice, we decide using EMV.

Finally we calculate EVPI using two different methods.

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.