Chapter 19 Decision Making Yandell – Econ 216

Chapter Goals After completing this chapter, you should be able to: Describe the decision environments of certainty and uncertainty Construct a payoff table and an opportunity-loss table Define and apply the expected value criterion for decision making Compute the value of perfect information Develop and use decision trees for decision making Yandell – Econ 216

Start Here You should begin this chapter with the overview material found here Click here to open pdf file Yandell – Econ 216

Decision Making Overview Decision Environment Decision Criteria Certainty Nonprobabilistic Uncertainty Probabilistic Yandell – Econ 216

The Decision Environment Certainty: The results of decision alternatives are known * Certainty Example: Must print 10,000 color brochures Offset press A: $2,000 fixed cost + $.24 per page Offset press B: $3,000 fixed cost + $.12 per page Uncertainty Yandell – Econ 216

The Decision Environment (continued) Uncertainty: The outcome that will occur after a choice is unknown Decision Environment Certainty Example: You must decide to buy an item now or wait. If you buy now the price is $2,000. If you wait the price may drop to $1,500 or rise to $2,200. There also may be a new model available later with better features. * Uncertainty Yandell – Econ 216

* Decision Criteria Decision Criteria Nonprobabilistic Decision Criteria: Decision rules that can be applied if the probabilities of uncertain events are not known. * Nonprobabilistic maximax criterion maximin criterion minimax regret criterion Probabilistic Yandell – Econ 216

* Decision Criteria Decision Criteria (continued) Decision Criteria Probabilistic Decision Criteria: Consider the probabilities of uncertain events and select an alternative to maximize the expected payoff of minimize the expected loss Nonprobabilistic * Probabilistic maximize expected value minimize expected opportunity loss Yandell – Econ 216

Features of Decision Making List Alternative Courses of Action (Possible Events or Outcomes) Determine ‘Payoffs’ (Associate a Payoff with Each Event or Outcome) Adopt Decision Criteria (Evaluate Criteria for Selecting the Best Course of Action) Yandell – Econ 216

List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree Yandell – Econ 216

A Payoff Table A payoff table shows alternatives, states of nature, and payoffs Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Yandell – Econ 216

Maximax Solution The maximax criterion (an optimistic approach): For each option, find the maximum payoff Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 1. Maximum Profit 200 120 40 Yandell – Econ 216

Greatest maximum is to choose Large factory Maximax Solution (continued) The maximax criterion (an optimistic approach): For each option, find the maximum payoff Choose the option with the greatest maximum payoff Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 2. Greatest maximum is to choose Large factory 1. Maximum Profit 200 120 40 Yandell – Econ 216

Maximin Solution The maximin criterion (a pessimistic approach): For each option, find the minimum payoff Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 1. Minimum Profit -120 -30 20 Yandell – Econ 216

Greatest minimum is to choose Small factory Maximin Solution (continued) The maximin criterion (a pessimistic approach): For each option, find the minimum payoff Choose the option with the greatest minimum payoff Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 2. Greatest minimum is to choose Small factory 1. Minimum Profit -120 -30 20 Yandell – Econ 216

Opportunity Loss Opportunity loss is the difference between an actual payoff for a decision and the optimal payoff for that state of nature Payoff Table Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 The choice “Average factory” has payoff 90 for “Strong Economy”. Given “Strong Economy”, the choice of “Large factory” would have given a payoff of 200, or 110 higher. Opportunity loss = 110 for this cell. Yandell – Econ 216

Opportunity Loss in $1,000’s (continued) Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Payoff Table Opportunity Loss Table Investment Choice (Alternatives) Opportunity Loss in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 110 160 70 90 140 50 Yandell – Econ 216

Minimax Regret Solution The minimax regret criterion: For each alternative, find the maximum opportunity loss (or “regret”) Opportunity Loss Table Investment Choice (Alternatives) Opportunity Loss in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 110 160 70 90 140 50 1. Maximum Op. Loss 140 110 160 Yandell – Econ 216

Minimax Regret Solution (continued) The minimax regret criterion: For each alternative, find the maximum opportunity loss (or “regret”) Choose the option with the smallest maximum loss Opportunity Loss Table Investment Choice (Alternatives) Opportunity Loss in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 110 160 70 90 140 50 1. Maximum Op. Loss 2. Smallest maximum loss is to choose Average factory 140 110 160 Yandell – Econ 216

Expected Value Solution The expected value is the weighted average payoff, given specified probabilities for each state of nature Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Suppose these probabilities have been assessed for these states of nature Yandell – Econ 216

Expected Value Solution (continued) Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Maximize expected value by choosing Average factory Expected Values 61 81 31 Example: EV (Average factory) = 90(.3) + 120(.5) + (-30)(.2) = 81 Yandell – Econ 216

Expected Opportunity Loss Solution Opportunity Loss Table Investment Choice (Alternatives) Opportunity Loss in $1,000’s (States of Nature) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 110 160 70 90 140 50 Minimize expected op. loss by choosing Average factory Expected Op. Loss (EOL) 63 43 93 Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2) = 63 Yandell – Econ 216

Value of Information Expected Value of Perfect Information, EVPI (also called Cost of Uncertainty) Expected Value of Perfect Information = Expected Value Under Certainty (EVUC) – Expected Value without information (EV) so: EVPI = EVUC – EV Yandell – Econ 216

Expected Value Under Certainty Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Expected Value Under Certainty (EVUC): EVUC = expected value of the best decision, given perfect information 200 120 20 Example: Best decision given “Strong Economy” is “Large factory” Yandell – Econ 216

Expected Value Under Certainty (continued) Investment Choice (Alternatives) Profit in $1,000’s (States of Nature) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Now weight these outcomes with their probabilities to find EVUC: 200 120 20 EVUC = 200(.3)+120(.5)+20(.2) = 124 Yandell – Econ 216

Value of Information Solution Expected Value of Perfect Information (EVPI) = Expected Value Under Certainty (EVUC) – Expected Value without information (EV) Recall: EVUC = 124 EV is maximized by choosing “Average factory”, where EV = 81 so: EVPI = EVUC – EV = 124 – 81 = 43 Yandell – Econ 216

Decision Tree Analysis A Decision tree shows a decision problem, beginning with the initial decision and ending will all possible outcomes and payoffs. Use a square to denote decision nodes Use a circle to denote uncertain events Yandell – Econ 216

Sample Decision Tree Large factory Average factory Small factory Strong Economy Large factory Stable Economy Weak Economy Strong Economy Average factory Stable Economy Weak Economy Strong Economy Small factory Stable Economy Weak Economy Yandell – Econ 216

Add Probabilities and Payoffs (continued) Strong Economy (.3) 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy 90 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 Decision (.3) Strong Economy 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Uncertain Events (States of Nature) Probabilities Payoffs Yandell – Econ 216

Fold Back the Tree Large factory Average factory Small factory Strong Economy (.3) EV=200(.3)+50(.5)+(-120)(.2)=61 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy EV=90(.3)+120(.5)+(-30)(.2)=81 90 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 (.3) Strong Economy EV=40(.3)+30(.5)+20(.2)=31 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Yandell – Econ 216

Make the Decision Large factory Average factory Small factory Strong Economy (.3) EV=61 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy EV=81 90 Maximum EV=81 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 (.3) Strong Economy EV=31 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Yandell – Econ 216

Utility Utility is the pleasure or satisfaction obtained from an action. Note: The utility of an outcome may not be the same for each individual. Yandell – Econ 216

Utility Example: each incremental $1 of profit does not have the same value to every individual: A risk averse person, once reaching a goal, assigns less utility to each incremental $1. A risk seeker assigns more utility to each incremental $1. A risk neutral person assigns the same utility to each extra $1. Yandell – Econ 216

Maximizing Expected Utility Making decisions in terms of utility, not $ Translate $ outcomes into utility outcomes Calculate expected utilities for each action Choose the action to maximize expected utility Yandell – Econ 216

Assessing Attitudes about Risk What is your risk preference? Risk averse? Risk neutral? Risk loving? Tools exist to assess your attitude toward risk Classroom assessment if time permits Yandell – Econ 216

Rationality: Making a Good Decision A good decision does not guarantee a good outcome A good outcome does not necessarily indicate a good decision Yandell – Econ 216

practice problem pdf file Try this practice problem: Click here to open practice problem pdf file Yandell – Econ 216

Chapter Summary Examined decision making environments certainty and uncertainty Reviewed decision making criteria nonprobabilistic: maximax, maximin, minimax regret probabilistic: expected value, expected opp. loss Computed the Value of Perfect Information (EVPI) Developed decision trees and applied them to decision problems Yandell – Econ 216