1. 1 Decision Analysis Scott Matthews 12-706 / 19-702

2. 12-706 and 73-3592 Administrative Comments  Group Project 1 Back - Average 91%  How graded?  High level thoughts - good on NPV  Some missed big picture - NPV?  HW 3 due next Wednesday

3. 12-706 and 73-3593 Commentary  It is trivial to do “economics math” when demand curves, preferences, etc. are known. Without this information we have big problems.  Unfortunately, most of the ‘hard problems’ out there have unknown demand functions.  We need advanced methods to find demand

4. 12-706 and 73-3594 Estimating Linear Demand Functions zAs above, sometimes we don’t know demand zFocus on demand (care more about CS) but can use similar methods to estimate costs (supply) zOrdinary least squares regression used yminimize the sum of squared deviations between estimated line and p,q observations: p = a + bq + e yStandard algorithms to compute parameter estimates - spreadsheets, Minitab, S, etc. yEstimates of uncertainty of estimates are obtained (based upon assumption of identically normally distributed error terms). zCan have multiple linear terms

5. 12-706 and 73-3595 Also - Log-linear Function zq = a(p) b (hh) c ….. zConditions: a positive, b negative, c positive,... zIf q = a(p) b : Elasticity interesting = (dq/dp)*(p/q) = abp (b-1) *(p/q) = b*(ap b /ap b ) = b. yConstant elasticity at all points. zEasiest way to estimate: linearize and use ordinary least squares regression (see Chap 12) yE.g., ln q = ln a + b ln(p) + c ln(hh)..

6. 12-706 and 73-3596 Log-linear Function  q = a*p b and taking log of each side gives: ln q = ln a + b ln p which can be re-written as q’ = a’ + b p’, linear in the parameters and amenable to OLS regression.  Alternative is maximum likelihood - select parameters to max. chance of seeing obs.

7. 12-706 and 73-3597 Maglev Log-Linear Function  q = a*p b - From above, b = -0.3, so if p = 1.2 and q = 20,000; so 20,000 = a*(1.2) -0.3 ; a = 21,124.  If p becomes 1.0 then q = 21,124*(1) -0.3 = 21,124.  Linear model - 21,000  Remaining revenue, TWtP values similar but NOT EQUAL.

8. 12-706 and 73-3598 Structuring Decisions  All about the objectives (what you want to achieve)  Decision context: setting for the decision  Decision: choice between options (there is always an option, including status quo)  Waiting for more information also an option  Uncertainty: as we’ve seen, always exists  Outcomes: possible results of uncertain events  Many uncertain events lead to complexity

9. 12-706 and 73-3599 Structuring Decisions (2)  Can use:  Fundamental objective hierarchy.  Influence diagrams.  Decision Trees  Risk Profiles

10. 12-706 and 73-35910 Fundamental Objectives Hierarchy Increase Lifetime Earnings Increase Current Salary Find New JobGet a Raise Update ResumeNetworkDo a Better Job Marry RichGo to School UndergradGrad School

11. 12-706 and 73-35911 Influence Diagram/Decision Trees  Probably cause confusion. If one confuses you, do the other.  Important parts: Decisions Chance Events Consequence/payoff Calculation/constant

12. 12-706 and 73-35912 Influence Diagram Lifetime Earnings Work High Salary Get a Raise Find a Better Job Marry Rich Go to School Undergrad Grad School

13. 12-706 and 73-35913 Other Notes  Chance node branches need to be mutually exclusive/exhaustive  Only one can happen, all covered  “One and only one can occur”  Timing of decisions along the way influences how trees are drawn (left to right)  As with NPV, sensitivity analysis, etc, should be able to do these by hand before resorting to software tools.

14. 12-706 and 73-35914 Solving Decision Trees  We read/write them left to right, but “solve” them right to left.  Because we need to know expected values of options before choosing.  Calculate values for chance nodes  Picking best option at decision nodes  We typically make trees with “expected value” or NPV or profit as our consequence  Thus, as with BCA, we choose highest value.

15. 12-706 and 73-35915 Texaco vs. Pennzoil Counteroffer $5 Billion Texaco Counteroffer $3 Billion Refuse Settlement Amount ($ Billion) Accept $2 Billion 2 Texaco Accept $5 Billion 5 Texaco Refuses Counteroffer Final Court Decision 10.3 5 0 Final Court Decision 10.3 5 0 Accept $3 Billion 3 (0.17) (0.5) (0.33) (0.2) (0.5) (0.3) (0.2) (0.5) (0.3)

16. 12-706 and 73-35916 To Solve the Tree  Solve from right to left:  At chance node multiply monetary value to probability and add them.  At choice node choose highest value. EMV for Simple Texaco vs. Pennzoil Tree: $4.63 Billion

17. 12-706 and 73-35917 Risk Profiles  Risk profile shows a distribution of possible payoffs associated with particular strategies.  A strategy is what you plan to do going in to the decision. Holds your plans constant, allows chances to occur  Only eliminate things YOU wouldn’t do, not things “they” might not do.  Its not just finding the NPV of a branch.

18. 12-706 and 73-35918 Risk Profiles (cont.)  Let’s think about the “subset” of the Texaco decision tree where we are only curious about the uncertainty/risk profile associated with various strategies to consider.  These represent the riskiness of each option  There are only 3 “decision strategies” in the base Texaco case:  Accept the $2 billion offer (topmost branch of 1st dec. node)  Counteroffer $5 Billion, but plan to refuse counteroffer (lower branch of 1st node, upper branch of second)  Counteroffer $5B, but plan to accept counteroffer (lower branch of both decision nodes)

19. 12-706 and 73-35919 Texaco vs. Penzoil, Again  Risk profile for “Accept $2 Billion” is obvious - get $2B with 100% chance.

20. 12-706 and 73-35920 Risk Profile: Counteroffer $5, accept $3 billion  Below is just the part of original tree to consider when calculating the risk profile: Counteroffer $5 Billion Texaco Counteroffer $3 Billion Texaco Accept $5 Billion 5 Texaco Refuses Counteroffer Final Court Decision 10.3 5 0 Accept $3 Billion 3 (0.17) (0.5) (0.33) (0.2) (0.5) (0.3)

21. 12-706 and 73-35921 Texaco vs. Pennzoil, continued

22. 12-706 and 73-35922 Cumulative Risk Profiles  Graphs of cumulative distributions  Percent chance that “payoff is less than x”

23. 12-706 and 73-35923 Dominance  To pick between strategies, it is useful to have rules by which to eliminate options  Let’s construct an example - assume minimum “court award” expected is $2.5B (instead of $0). Now there are no “zero endpoints” in the decision tree.

24. 12-706 and 73-35924 Dominance Example  CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

25. 12-706 and 73-35925 Next Class  Value of Information.  Facility Case Due