Module 5 Decision Theory

Module 5 Part 2: Decision Theory

BUS216 “Probability & Statistics for Business and Economics”Tidewater Community CollegeLinda S. Williams, MBA, MSAProfessor, Business Administration


Decision-Making under CertaintyDecision-Making under Uncertainty

Decision-Making under Risk

Goals: 1. Maximize Returns 2. Minimize Loss3. 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


Module 5 Part 2: Decision TheoryPayoff 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)





Module 5 Part 2: Decision TheoryDecision Making Under Certainty

• State of Nature is known• Select Decision Alternative with the highest payoff

…. And this happens when ?????

ALMOST NEVER!

Module 5 Part 2: Decision TheoryDecision 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

Module 5 Part 2: Decision TheoryMaximax 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

Module 5 Part 2: Decision TheoryMaximin 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

Module 5 Part 2: Decision TheoryHurwicz 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

Module 5 Part 2: Decision TheoryMinimax 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

Module 5 Part 2: Decision TheoryDecision 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

Module 5 Part 2: Decision TheoryExpected 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

Module 5 Part 2: Decision TheoryExpected 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

Education

Module 5 Decision Theory