ch.7 Decision theory and decision maker .ppt
- 1. Ch 7 Decision theory Learning objectives : After completing this chapter, you should be able to : 1 . Outline the characteristics of a decision theory approach to decision making . 2 . Describe and give examples of decisions under certainty, risk, and complete uncertainty . 3 . Cons tract a payoff table . 4 . Use decision trees to lay out decision alternatives and possible consequences of decisions .
- 2. Summary Decision theory is a general approach to decision making. It is very useful for a decision maker who must choose from a list of a alternative. Knowing that one of a number of possible future states of nature will occur and that this will have an impact on the payoff realized by a particular alternative .
- 3. Glossary Payoff: a table that shows the payoff for each alternative for each state of nature . Risk: A decision problem in which the state of nature have probability associated which their occurrence . Uncertainty: Refers to a decision problem in which probabilities of occurrence for the various states of nature one unknown . Decision tree: A schematic representation of a decision problem that involves the use of branches and nodes .
- 4. Ch.7 Decision theory 1 . Decision making A. Under certainty . B. Under complete uncertainty . C. Under risk . 2 . Decision tree A. Expected monetary value model . B. Expected net present value model .
- 5. Decision theory Decision theory problems are characterized by the following : 1 . A list of alternatives . 2 . A list of possible future states of natures . 3 . Payoff associated with each alternative / state of nature combination . 4 . An assessment of the degree of certainty of possible future events . 5 . A decision criterion .
- 6. The payoff table A payoff table is a device a decision maker can use to summarize and organize information relevant to particular decision . A payoff table includes : 1 . A list of the alternatives . 2 . The possible future state of nature . 3 . The payoffs associated with each of the alternative/ state of nature combinations . 4 . If probabilities for the state of nature are available, these can also be listed .
- 7. Table : General format of a decision table . State of nature alternatives V11 V12 V13 V21 V22 V23 V31 V32 V33 A B C S1 S2 S3 Where : A , B , C = alternatives . Sn = the n th state of nature . Vij = the value of payoff that will be realized if alternative X is chosen and event j occurs .
- 8. Example -: Suppose an investor must decide on an alternative to invest his/ her money to maximize profit or revenue. He /she has the following alternative : A: bonds B: socks C: deposits suppose in the case of investment the profitability influences with economic development. Suppose that the investor views the possibilities as : 1 . Economic growth. 2. Economic decline. 3. Economic inflation . Suppose the payoff are alternatives State of natures . 12 6 - 3 10 7 - 2 10 10 10 A B C 1 2 3 Initiate payoff tableau
- 9. Investment payoff tableau State of nature alternatives Eco. S1 growth Eco. S2 decline Eco. S3 inflation Bonds A Bonds B Bonds C 12 10 10 6 7 10 - 3 - 2 10 Note :- If the investor choose A – S1 , that is, he /she realizes a profit of $1200 as a returns on bonds . If the investor choose A – S3 that is, he /she realize a losses of $300 .
- 10. 1 . Decision making under certainty . The simplest of all circumstances occurs when decision making takes place in an environment of complete certainty . In our case the investor should bonds because it has the highest estimated payoff of 12 in that column .
- 11. 2 . Decision making under complete uncertainty . Under complete uncertainty, the decision maker is ether unable to estimate the probabilities for the occurrence of the different state of nature, or else he/ she lacks confidence in available estimate of probabilities . That is, probabilities are not included in the analysis . To solve a problem, we shall consider 5 approaches to decision making under complete uncertainty : 1 . Maxi Max . 2 . Maxi Min . 3 . Equally likely . 4 . Criterion of realism . 5 . Min Max regret .
- 12. 1 . Maxi Max approach -: It is an optimistic view point . It’s procedures are simple : choose the best payoff for each alternative and then choose the maximum one among them . Consider the example : 4 16 12 6 6 10 - 1 4 15 A B C S1 S2 S3 Best payoff 16 10 15 maximum
- 13. 2 . Maxi Mix approach -: It is an pessimistic view point . It’s procedures are simple : choose( worst ) payoff for each alternative and then choose the maximum one among them . Consider the example : minimum 4 16 12 5 6 10 - 1 4 15 A B C S1 S2 S3 Worst payoff 4 5 - 1 maximum minimum
- 14. 3 . Equally likely approach : The decision maker should not focus on either high or low payoffs, but should treat all payoff ( actually, all states of nature ) as of they were equally likely averaging row payoffs accomplishes this . Consider the example : 4 16 12 5 6 10 - 1 4 15 A B C S1 S2 S3 Expected payoff 4 + 16 + 12 3 5 + 6 + 10 3 - 1 + 4 + 15 3 maximum = 12.40 = 7.00 = 6.30
- 15. 4 . Criterion of realism : Many people views maxi min criterion as pessimistic because they believe that the decision maker must assume that the worst will occur . The opposite views for maxi max, they are optimistic . Criterion of realize combine the tow opposite views points . So we need to know the percent of optimistic and the percent of pessimistic . Suppose that 60% optimistic . 40% pessimistic . Expected value = worst payoff ( % pessimistic ) + best payoff ( % optimistic )
- 16. Consider the example : 4 16 12 5 6 10 - 1 4 15 A B C S1 S2 S3 Worst payoff Best payoff 4 16 5 10 - 1 15 A = 4 ( .40 ) + 16 ( .60 ) = 11.2 maximum B = 5 ( .40 ) + 10 ( .60 ) = 8.0 C = -1 ( .40 ) + 15 ( .60 ) = 8.6
- 17. 5 . Mini max regret approach -: In order to use this approach, it is necessary to develop an opportunity loss table . The opportunity loss reflects the difference between each payoff and the best payoff in the column ( given the state of nature ) . Hence, opportunity loss amounts are found by identifying the best payoff in a column and then subtracting each of the other values in the column from that payoff . Go to the example
- 18. Opportunity loss table for investment problem . Original payoff table : Opportunity loss table : 4 16 12 5 6 10 - 1 4 15 A B C S1 S2 S3 5 – 4 = 1 A B C S1 S2 S3 16 – 16 = 0 15 – 12 = 3 5 – 5 = 0 16 – 6 = 10 15 – 10 = 5 5 - – 1 = 6 16 – 4 = 12 15 – 15 = 0 1 0 3 0 10 6 6 12 0 A B C S1 S2 S3 Maximum loss 3 10 12 Minimum
- 19. 3 . Decision making under risk . The essential difference between decision making under complete uncertainty and decision making partial uncertainty ( risk ) is the presence of probabilities . Under risk the manager know the probabilities for the occurrence of various state of natures . 1 . The probabilities may be subjective estimates from manager, or 2 . From experts in a particular field , or . 3 . They may reflect historical frequencies .
- 20. The model to be used for solving decision making problems under risk. Is as follows : Expected monetary value : Emvi = PJVIJ Where : Emvi = The expected monetary value for the i th alternative . Pj = The probability of the j th state of nature . Vij = The estimated payoff for alternative i under state of nature j . Go to example M i = 1 K
- 21. Example : decision under risk 4 16 12 5 6 10 - 1 4 15 A B C S1 S2 S3 Probability .2 .2 .3 = 1.0 EmvA = .2 ( 4 ) + .5 ( 16 ) + .3 ( 12 ) = 12.40 EmvB = .2 ( 5 ) + .5 (6 ) + .3 ( 15 ) = 7.00 EmvC = .2 ( -1 ) + .5 ( 4 ) + .3 ( 15 ) = 6.30 If you want to compute Emvi for expected opportunity loss Co to the example Maximum
- 22. Example : Investment problem, opportunity losses . 1 0 3 0 10 5 6 12 0 A B C S1 S2 S3 Probabilities .2 .5 .3 EolA = .2 ( 1 ) + .5 (0 ) + .3 ( 3 ) = 1.1 EolB = .2 ( 0 ) + .5 (10 ) + .3 ( 5 ) = 6.5 EolC = .2 ( 6 ) + .5 (12 ) + .3 ( 0 ) = 7.2 Minimum Note :- Eol , expected opportunity loss
- 23. Decision tree Sometimes are used by decision makers to obtain a visual picture of decision alternatives and their possible consequences . A tree is composed of 1 . Squares decision point . 2 . Circles chance events . 3 . Lines state of natures . See the figure : State of nature Alternative Decision point
- 24. To solve a decision tree problem we use two model : 1 . Expected monetary value model Emvi 2 . Expected net present value model Enpvi Let’s go to examples
- 25. Back to our example that related to investment decision : Just we need additional info . The duration of investment just one year . . 2 growth . 5 Decline . 3 Inflation 4 16 12 . 2 growth . 5 Decline . 3 Inflation 5 6 10 . 2 growth . 5 Decline . 3 Inflation - 1 4 15 12.4 7.00 6.30 A B C bonds stocks Deposit 1 Year Solution by Emvi EmvA = .2 ( 4 ) ( 1 ) = .8 . = 5 ( 16 ( ) 1 = ) 8.00 . = 3 ( 12 ( ) 1 = ) 3.6 12.4 Maximum And so on for B and C
- 26. Using Enpvi to solve decision tree problems . Note -: 1 . You need to have with you net present value tables single, and annuity tables. And you can use them . Or 2 . You need to have net present value equations and you can apply it . Let’s go examples
- 27. Example -: Suppose that you have two alternatives for investment : 1 . Building a small size plant to produce a product, the initial cost $ 400,000 : If demand is good revenues will be $ 10,000 the probability of good demand is 60% . If demand is stable revenues will be $ 8,000 the probability of stable demand is 30% . If demand is worse revenues will be $ 5,000 the probability is 10% Go to the another alternative
- 28. 2 . Building a medium size plant for the same purpose, initial cost $ 600,000 . Revenues depend on the demand status : Good demand 60% revenues $ 12,000 Stable demand 30% revenues $ 9,000 Worse demand 10% revenues $ 4,000 Additional info . 1 . Interest rate 7% . 2 . period 5 years . 3 . Revenues due at the end of each period . 4 . At the end of year 5 you will sell the first plant $600,000 , and the second plant with $ 800,000 . Choose the best alternative ? Go to the solution .
- 29. Solution : Small plant Medium plant 1 . Decision tree Good demand 5 $/ 10,000 Stable demand 5 $/ 8,000 Worse demand 5 $/ 5,000 60% 30% 10% Good demand 5 $/ 12,000 Stable demand 5 $/ 9,000 Worse demand 5 $/ 4,000 60% 30% 10% $ 400,000 $ 600,000 At the end of year 5 you will have $ 600,000 ( Disposal value ) At the end of year 5 you will have $ 800,000 ( Disposal value )
- 30. 2 . Computation using Enpvi : Info . payoff P NPV ENPVi x x = Small plant 10,000 . 60 4.100 24.600 Good demand 8,000 . 30 4.100 9.840 Stable demand 5,000 . 10 4.100 2050 Worse demand Disposal value 600.000 1 . 713 427,800 Payoff M 464.290 - Cost ( 400,000 ) Enpv 64,290 Initial cost From the annuity table 5 years 7% interest rate . From the single amount table 7% interest rate at the end of year 5 .
- 31. Medium plant Good demand 12,000 . 60 4.100 29520 Stable demand 9,000 . 30 4.100 11070 Worse demand Disposal value 800.000 1 . 713 570400 Payoff M 612630 - Cost ( 600,000 ) Enpv 12,630 4,000 . 10 4.100 1640 Small plant is the beat because of the highest amount than medium plant .
- 32. Note :- Solving NPv by equations present value of a single a mount . PVIFr,n = 1 ( 1 + R ) n Present value of an annuity PVIFAr,n = 1 ( 1 + R ) n M n t = 1 At the end period At the end period From table Pv = FVn X PVIFr,n PVAn = PMT X PVIFAr,n
- 33. Note :- If the amount due at 1/1 ( annuity ) Use : PVA = PMT X X 1 + R R 1 - 1 ( 1 + R ) n Or . Suppose the payoff of 5 years due at 1/1 ( annuity ) From the table : 4 year at the end 31/12 1 year at the 1/1 4 years at 13/12 R = 8% 3.312 1.000 + 4.312 at 1/1