Demonstration: Decision-Making Under Uncertainty

1. Demonstration: Decision-Making Under Uncertainty

2. We will demonstrate the principles using a simple (but real) example. • This is a personal investment decision. • The outcome is uncertain. • The potential gains/losses are real. What is the most that you are willing to invest? 1.03 • Decision-Making Under Uncertainty

3. MasterCard VISA Thumbtack Sweepstakes Rules 1. The selected participant plays the game once. 2. The cost to play is 20. 3. Payment is cash or check; no refunds. 4. I will “flip” a thumbtack. 5. The player calls: “Point up” “Point down” 6. If the call is correct, the player wins and keeps 100. 7. If the call is incorrect, the player wins nothing. 8. I keep the amount paid to play, regardless of the outcome. 1.03 • Decision-Making Under Uncertainty

4. Decision Uncertainty Outcome Net Profit Correct Call 100 80 Invest – 20 Incorrect Call 0 – 20 Don’t Invest 0 0 Time Decision Uncertainty A decision tree organizes and displays important factors of a decision in chronological sequence. 1.03 • Decision-Making Under Uncertainty

5. We define a decision as an “irrevocable” allocation of resources. We have a certificate acknowledging this first “decision” of the day. 1.03 • Decision-Making Under Uncertainty

6. Correct Call Incorrect Call Probabilities quantify the player’s judgment about the likelihood of winning. This uncertain situation is called a “deal” or a “lottery.” Probability = p Probability = 1 – p 1.03 • Decision-Making Under Uncertainty

7. Deal Uncertainty Outcome Correct Call 100 p = 1 – p = Incorrect Call 0 To evaluate the tree, we must establish a value for the deal, assuming that we’ve made the investment. To value the deal going forward, ignore the “sunk” 20; that’s behind us now. Decision Uncertainty Outcome Correct Call 100 p = Invest 1 – p = – 20 Incorrect Call 0 Don’t Invest 0 1.03 • Decision-Making Under Uncertainty

8. The value of the deal is the player’s minimum selling price or “certain equivalent.” The player is indifferent between having the deal or its certain equivalent. Deal Uncertainty Outcome Correct Call CertainEquivalent 100 p = 1 – p = Incorrect Call 0 1.03 • Decision-Making Under Uncertainty

9. Another way to value the deal is to calculate its “expected value” (probability-weighted average). The expected (or “mean”) value is the average return from each flip if it were repeated many times. Deal Uncertainty Outcome Correct Call ExpectedValue 100 p = 1 – p = Incorrect Call p x 100 + (1 – p) x 0 0 1.03 • Decision-Making Under Uncertainty

10. Expected Value RiskAverse RiskNeutral RiskPreferring The difference between “expected value” and “certain equivalent” reflects attitude toward risk. This is a matter of preference; there is no “correct” risk attitude. Monetary Value Certain Equivalent Risk Attitude 1.03 • Decision-Making Under Uncertainty

11. Decision Uncertainty Outcome Correct Call 100 p = No Info 1 – p = Incorrect Call 0 Buy Information ? –? Is it worthwhile to gather information to reduce or to eliminate uncertainty? What is the most that our player should pay for perfect information? 1.03 • Decision-Making Under Uncertainty

12. Decision Uncertainty Outcome Correct Call 100 CertainEquivalent p = No Info 1 – p = Incorrect Call 0 Value Added Buy PerfectInformation Correct Call 100 Perfect information about the outcome of the flip guarantees winning the 100. –? p = 1.0 Here the value added by perfect information is 100 – the certain equivalent. How many opportunities do you have to buy perfect information in your business? 1.03 • Decision-Making Under Uncertainty

13. Perfect information may not be available. Here are imperfect sources. • Experiments—5 trial flips of the tack • Opinion polls • Experts • Mathematical models SURVEY 1.03 • Decision-Making Under Uncertainty

14. Point up? Point down? What is your call? 1.03 • Decision-Making Under Uncertainty

15. Good Outcomes Good Decisions 40 .6 .4 –6 15 .7 .3 4 Balances the probabilities of good and bad outcomes consistent with preferences Preferred Results We must distinguish between good decisions and good outcomes. 1.03 • Decision-Making Under Uncertainty

16. Decisions with Certainty Decisions with Uncertainty Correct Invest Correct Invest Incorrect Don’t Invest Don’t Invest Good decisionsguaranteegood outcomes. Good decisionsdo not guaranteegood outcomes. Making good decisions may not lead to good outcomes. The goal of decision analysis is make the best decisions in the face of uncertainty. 1.03 • Decision-Making Under Uncertainty

17. ... 30% ... Invest Buy Info. Several insights emerge from the demonstration. • A decision is an irrevocable allocation of resources. • Probability is the quantitative language for communicating about uncertainty. • Probabilities represent judgment, which includes experience and information. • The value of an uncertain deal depends on its characteristics and one’s attitude toward risk. • The economic value of gathering more information can be calculated before making a decision. • We must distinguish between the quality of the decision and its outcome. 1.03 • Decision-Making Under Uncertainty