# 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.

#### Solution Preview

Please see attachment for properly formatted copy.

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.