Fundamentals of Decision Theory Models

Deciding Between Job Offers• Company A• In a new industry that could boom or bust.• Low starting salary, but could increase rapidly.• Located near friends, family and favorite sports team.

• Company B• Established firm with financial strength and commitment

to employees.• Higher starting salary but slower advancement

opportunity.• Distant location, offering few cultural or sporting

activities.

• Which job would you take?

Good Decisions vs. Good Outcomes

• A structured approach to decision making can help us make good decisions, but can’t guarantee good outcomes.

• Good decisions sometimes result in bad outcomes.

Introduction

Decision theory is an analytical and systematic way to tackle problems

A good decision is based on logic.

The Six Steps in Decision Theory

1. Clearly define the problem at hand

2. List the possible alternatives

3. Identify the possible outcomes & criteria

4. List the payoff or profit of each combination of

alternatives and outcomes

5. Select one of the mathematical decision theory models

6. Apply the model and make your decision

Types of Decision-Making Environments

Type 1: Decision-making under certaintydecision-maker knows with certainty the consequences of every alternative or decision choice. (You know exact outcome; eg Savings Account)

Type 2: Decision-making under riskdecision-maker does know the probabilities of the various outcomes (You know the probability of each outcome; e.g. roll of die)

Type 3: Decision-making under uncertaintydecision-maker does not know the probabilities of the various outcomes (You know nothing, it is a wild guess at best)

Decision-Making Under Risk

n nature, of states ofnumber the to 1 j where

)P(S*Payoff i) ativeEMV(Alternn

1jjSj

=

å==

Expected Monetary Value: (Sum of the probabilities and outcome)

ExampleYou recently inherited $1,000 and are considering investing it in varied financial instruments.After Analyzing the economy (possibility of it being good or poor ) and the returns you can make in these conditions, you develop the following payoff table…

Decision Table

State Of Nature

Decision Alternative Good Economy Poor Economy

Portfolio 1 (high risk) 80 -20

Portfolio 2 (med risk) 30 20

Portfolio 3 (low risk) 23 23

Probability 0.3 0.7

Which portfolio should you invest in, that will maximize your returns?

Decision Table

State Of Nature

Decision Alternative Good Economy Poor Economy EMV

Portfolio 1 (high risk) 80 -20 10

Portfolio 2 (med risk) 30 20 23

Portfolio 3 (low risk) 22 22 22

Probability 0.3 0.7

What is the maximum amount that should be paid for perfect forecast of the economy?

Expected Value of Perfect Information (EVPI)

EVPI places an upper bound on what one would pay for additional information

EVPI is the expected value with perfect information minus the maximum EMV

EVPI = EV|PI - maximum EMV

EVPI

State Of Nature

Decision Alternative Good Economy Poor Economy EMV

Portfolio 1 (high risk) 80 -20

Portfolio 2 (med risk) 30 20 23

Portfolio 3 (low risk) 22 22

Probability 0.3 0.7

EVPI = Expected Value with Perfect Information - max(EMV) =

[80 0.3 + 22 0.7] – 23 = $16.4

Expected Opportunity LossEOL is the cost of not picking the best solution

EOL = Expected Regret

Work it the same way as EMV but just use the regret instead of payoffs.

EOL Table State Of Nature

Decision Alternative Good Economy Poor Economy EOL

Portfolio 1 (high risk) 80 – 80 = 0 22 – (-20) = 42

Portfolio 2 (med risk) 80 – 30 = 50 22 – 20 = 2

Portfolio 3 (low risk) 80 – 22 = 58 22 – 22 = 0

Probability 0.3 0.7

EOL Table State Of Nature

Decision Alternative Good Economy Poor Economy EOL

Portfolio 1 (high risk) 0 42 29.4

Portfolio 2 (med risk) 50 2 16.4

Portfolio 3 (low risk) 58 0 17.4

Probability 0.3 0.7

Sensitivity Analysis

EMV(high risk) = $80P + (-$20) (1-P)

EMV(med risk) = $30P + $20(1-P)

EMV(low risk) = $22P + $22(1-P)

Sensitivity Analysis - continued

-20

-10

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.42

EMV (Med Risk)

EMV(H

igh R

isk)

0.4440.2

EMV(low Risk)

Decision Making Under Uncertainty

Maximax

Maximin

Equally likely (Laplace)

Criterion of Realism

Minimax Regret

Decision Making Under UncertaintyMaximax - Choose the alternative with the maximum output

States of Nature

Favorable Mkt ($)

Unfavorable Mkt ($)

Maximax

Construct Large Plant

200,000 -180,000 200,000

Construct Small Plant

100,000 -20,000 100,000

Do Nothing 0 0 0

Decision Making Under UncertaintyMaximin - Choose the alternative with the maximum minimum output

States of Nature

Favorable Mkt ($)

Unfavorable Mkt ($)

Maximin

Construct Large Plant

200,000 -180,000 -18,000

Construct Small Plant

100,000 -20,000 -20,000

Do Nothing 0 0 0

Decision Making Under UncertaintyEqually likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV

States of Nature

Favorable Mkt ($)

Unfavorable Mkt ($)

Equally Likely

Construct Large Plant

200,000 -180,000 10,000

Construct Small Plant

100,000 -20,000 40,000

Do Nothing 0 0 0

Probabilities 0.5 0.5

Decision Making Under UncertaintyCriterion of Realism (Hurwicz):CR = *(row max) + (1-)*(row min)

=0.8

States of Nature

Favorable Mkt ($)

Unfavorable Mkt ($)

CR

Construct Large Plant

200,000 -180,000 124,000

Construct Small Plant

100,000 -20,000 76,000

Do Nothing 0 0 0

Decision Making Under UncertaintyMinimax - choose the alternative with the minimum maximum Opportunity Loss - this is using EOL table

States of Nature

Favorable Mkt ($)

Unfavorable Mkt ($)

Minimax Regret

Construct Large Plant

0 180,000 180,000

Construct Small Plant

100,000 20,000 20,000

Do Nothing 200,000 0 200,000

Probabilities 0.5 0.5

Summary

Decision theory

Decision Making under Risk

Decision Making under Uncertainty