Module 5 Decision Theory

Module 5 Part 2: Decision Theory
BUS216 “Probability & Statistics for Business and Economics”
Tidewater Community College
Linda S. Williams, MBA, MSA
Professor, Business Administration

Decision-Making under Certainty
Decision-Making under Uncertainty
Decision-Making under Risk
Goals:
1. Maximize Returns
2. Minimize Loss
3. Minimize Regret

Components of All Decisions:
• Decision Alternatives
• These are the options or choices open to any decision maker.
• Identification of possible alternatives is the starting point for all
decision theory
• States of Nature
• These are any condition in “nature” that can occur after a decision
has been made
• The conditions affect the outcome of the decision in either a
positive, neutral or negative way
• The decision maker does not control the States of Nature
• Payoffs
• These are the rewards for any given decision alternative
• Payoffs can range in size and in some instances may be a loss

Payoff Tables
State of
Nature
(S1)
State of
Nature
(S2)
State of
Nature
(S3)
State of
Nature
(S4)
Decision
Alternative
(d1)
Payoff (P1,1) Payoff (P1,2) Payoff (P1,3) Payoff (P1,4)
Decision
Alternative
(d2)
Decision
Alternative
(d3)

Decision Making Under Certainty
• State of Nature is known
• Select Decision Alternative with the highest payoff
…. And this happens when ?????
ALMOST NEVER!

Decision Making Under Uncertainty
• The decision maker does not know which state of
nature will occur
• The decision maker does not know the probability
of the various states of nature occurring
• Approaches to decision making under uncertainty
depend upon the criteria for the decision and the
decision maker’s outlook
• Payoff Tables are used to determine possible payoffs
under various states of nature

Maximax Criterion
• Optimistic approach where decision maker bases action
on the “best case” scenario”
• Isolate the highest payoff under each decision alternative
• Select the decision alternative that provides the highest
payoff of the maximums
• Often called “best of the best” approach to decision
making

Maximin Criterion
• This is a pessimistic approach to decision making
• The assumption is that the “worst” will occur and so
the decision is made to minimize the damage
• Determine the smallest payoff under each decision
alternative
• Select the “best” of these worst case scenario payoffs
• We refer to this as “maximizing the minimum” return

Hurwicz Criterion
• This is a “middle of the road” approach
• This criterion selects the maximum payoff and the
minimum payoff for each decision alternative
• α =the optimism with a value between 0 and 1 with 1
being the MOST optimistic
• Multiply the maximum payoff by α
• Multiply the minimum payoff by 1 – α
• Sum the weighted products for each decision
alternative
• Select the maximum weighted value and the
corresponding decision alternative

Minimax Regret Strategy
• Based on lost opportunity because the wrong decision
was made and payoff was not maximized
• Transform the Decision Table into an Opportunity Loss
Table in order to apply the Minimax Regret criterion
• Determine the highest payoff for each decision under the
State of Nature
• Subtract the payoff for each decision alternative from the
highest payoff. This is the “regret”
• Replace the payoffs with the “regret” or opportunity
losses creates the opportunity loss table
• Then determine the maximum regret for each decision
alternative and select the smallest regret available

Decision Making Under Risk
• The decision maker does not know which state of
nature will occur
• The decision maker knows the probability of the
various states of nature occurring
• Payoff Tables are used to determine possible
payoffs under various states of nature
• Decisions are made based on the long-run average
return for a decision, based on the probability of
the various states of nature

Expected Monetary Value (EMV)
• Each payoff under each state of nature is now
associated with a probability
• Find the EMV of each Decision Alternative: (Payoff) X
(Probability of that State of Nature)
• Sum the products across the States of Nature to arrive
at the EMV of each alternative
• Select the decision alternative with the highest EMV
• The strategy of EMV is that it maximizes the return over
the “long run”
• It does not guarantee this return on a single investment

Expected Value of Perfect Information (EVPI)
• The EVPI is the value that a decision maker places on
knowing which state of nature will occur
• It is always presumed that the information is available
• It is always presumed that the information is accurate
• As long as the EVPI does not exceed the EMV, the decision
maker will pay for the information
EVPI = EMV with Perfect Information – EMV without
Information

• What is the value of knowing which state of nature
will occur?
• This is the difference between the payoff that would
occur if the decision maker knew which state of
nature would occur and the expected monetary payoff
from the best alternative when there is no information
available
• EVPI = Expected Monetary Payoff with Perfect
Information – Expected Monetary Payoff without
Information

• Expected Monetary Value without information =
highest payoff considering the probability of each
State of Nature
• Perfect Information: Highest Payoff under each State
of Nature weighted by the probability of that State of
Nature
• The difference between these two is the EVPI

Module 5 Decision Theory

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