# Oil---Uncertainty by akgame

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Oil---Uncertainty

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```									Decision Making Under Uncertainty
Input: Alpha = Decision Drill Sell

Oil Speculation
We own a piece of land that we believe may contain oil. We have two choices: drill or sell. If we drill, it costs \$100K. If oil is found, our revenue will be \$800K. If we sell the land, we get a profit of \$90K. Determine the maximax, maximin, equal likelihood, and Hurwicz (using alpha = 0.25) decisions.

States of Nature Dry Oil

All numbers are \$K

Calculations: Decision Drill Sell Output: Maximax decision Maximin decision Equal Likelihood Hurwicz Maximum 0.00 0.00 Minimum 0.00 0.00 Equal Likelihood #DIV/0! #DIV/0! Hurwicz 0.00 0.00 Decision Drill Sell

0.00 0.00 #DIV/0! 0.00

Drill Drill #DIV/0! Drill

Oil Speculation
First determine EVWPI by taking the maximum payout over all decisions for each state of nature and multiple that number by it's associated probability. Add all of these up. Next, we need to find the EVWOPI. This value is found by taking the maximum of the EV's for each decision. Now, to find EVPI, simply subtract EVWOPI from EVWPI.

Input: States of Nature Decisions Probability Drill Sell Dry 0.75 Oil 0.25 Expected Value 0 0 Decision Drill Sell

All numbers are \$K
Output: Decision EVWPI EVWOPI EV of Perfect Information Drill \$0.00 \$0.00 \$0.00

Formulae:

Expected Value Expected Value of Perfect Information

EV(x ) =  p x i  x i
i 1

n

EVPI = expected value with perfect information  expected value without perfect information.

Now we have the opportunity to conduct a seismic survey (SS) of the plot for \$30K. There is a 30% chance the SS will be favorable (FSS) and a 70% chance it will be unfavorable (USS). Construct a decision tree to determine if the SS should be conducted.

All numbers are \$K

? 6 Drill ? Sell USS (0.7) ? 2
SS

Oil (1/7)

670

-130 Dry (6/7)

60

? ? Drill 7

Oil (0.5)

670

?

FSS (0.3) Sell

Dry (0.5)

-130

60

? ? No SS Drill
8

Oil (0.25)

700

Dry (0.75) Sell

-100
90

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