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Problem_Session_6_-_Example_1

# Problem_Session_6_-_Example_1 - Decision Tree for Lottery...

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Unformatted text preview: Decision Tree for Lottery Deals 0.000 500 0.7 Red Ball Deal A 0.65 \$645 0.3 White Ball 0.40 0.7 Red Ball >>> Deal B 2 0.70 \$700 0.70 \$700 0.3 White Ball 0.00 Deal C 0.50 \$500 1.00 70 0.75 ottery Deals ---> Value of Payoff 1 Unfold to reveal \$0 sensitivity \$10 to Value \$20 of Payoff 1 \$30 \$-value \$750 u-value 0.75 \$40 \$50 \$60 \$70 \$80 \$90 \$100 \$110 \$120 \$130 \$140 \$150 \$160 \$170 \$180 \$190 \$200 \$210 \$220 \$230 \$240 \$250 \$260 \$270 \$280 \$290 \$300 \$310 \$320 \$330 \$340 \$350 \$360 \$370 \$380 \$390 Deal A \$645 \$120 \$127 \$134 \$141 \$148 \$155 \$162 \$169 \$176 \$183 \$190 \$197 \$204 \$211 \$218 \$225 \$232 \$239 \$246 \$253 \$260 \$267 \$274 \$281 \$288 \$295 \$302 \$309 \$316 \$323 \$330 \$337 \$344 \$351 \$358 \$365 \$372 \$379 \$386 \$393 \$400 0.40 \$1,000 1.00 \$0 0.00 \$500 0.50 \$400 \$410 \$420 \$430 \$440 \$450 \$460 \$470 \$480 \$490 \$500 \$510 \$520 \$530 \$540 \$550 \$560 \$570 \$580 \$590 \$600 \$610 \$620 \$630 \$640 \$650 \$660 \$670 \$680 \$690 \$700 \$710 \$720 \$730 \$740 \$750 \$760 \$770 \$780 \$790 \$800 \$810 \$820 \$830 \$400 \$407 \$414 \$421 \$428 \$435 \$442 \$449 \$456 \$463 \$470 \$477 \$484 \$491 \$498 \$505 \$512 \$519 \$526 \$533 \$540 \$547 \$554 \$561 \$568 \$575 \$582 \$589 \$596 \$603 \$610 \$617 \$624 \$631 \$638 \$645 \$652 \$659 \$666 \$673 \$680 \$687 \$694 \$701 \$840 \$850 \$860 \$870 \$880 \$890 \$900 \$910 \$920 \$930 \$940 \$950 \$960 \$970 \$980 \$990 \$1,000 \$708 \$715 \$722 \$729 \$736 \$743 \$750 \$757 \$764 \$771 \$778 \$785 \$792 \$799 \$806 \$813 \$820 Deal B \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 Deal C \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 ---> Best Unfold to ### reveal ### sensitivity ### to ### Proba of ### Red ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### Proba of Red 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 Deal A \$645 \$400 \$404 \$407 \$411 \$414 \$418 \$421 \$425 \$428 \$432 \$435 \$439 \$442 \$446 \$449 \$453 \$456 \$460 \$463 \$467 \$470 \$474 \$477 \$481 \$484 \$488 \$491 \$495 \$498 \$502 \$505 \$509 \$512 \$516 \$519 \$523 \$526 \$530 \$533 \$537 Deal B \$700 \$0 \$10 \$20 \$30 \$40 \$50 \$60 \$70 \$80 \$90 \$100 \$110 \$120 \$130 \$140 \$150 \$160 \$170 \$180 \$190 \$200 \$210 \$220 \$230 \$240 \$250 \$260 \$270 \$280 \$290 \$300 \$310 \$320 \$330 \$340 \$350 \$360 \$370 \$380 \$390 Deal C \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 Best ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 \$540 \$544 \$547 \$551 \$554 \$558 \$561 \$565 \$568 \$572 \$575 \$579 \$582 \$586 \$589 \$593 \$596 \$600 \$603 \$607 \$610 \$614 \$617 \$621 \$624 \$628 \$631 \$635 \$638 \$642 \$645 \$649 \$652 \$656 \$659 \$663 \$666 \$670 \$673 \$677 \$680 \$684 \$687 \$691 \$400 \$410 \$420 \$430 \$440 \$450 \$460 \$470 \$480 \$490 \$500 \$510 \$520 \$530 \$540 \$550 \$560 \$570 \$580 \$590 \$600 \$610 \$620 \$630 \$640 \$650 \$660 \$670 \$680 \$690 \$700 \$710 \$720 \$730 \$740 \$750 \$760 \$770 \$780 \$790 \$800 \$810 \$820 \$830 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$700 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 \$694 \$698 \$701 \$705 \$708 \$712 \$715 \$719 \$722 \$726 \$729 \$733 \$736 \$740 \$743 \$747 \$750 \$840 \$850 \$860 \$870 \$880 \$890 \$900 \$910 \$920 \$930 \$940 \$950 \$960 \$970 \$980 \$990 \$1,000 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ---> Unfold to reveal sensitivity to -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Deal A \$645 \$745 \$744 \$743 \$741 \$738 \$732 \$716 \$645 \$514 \$460 \$440 \$430 \$424 \$420 \$417 Deal B \$700 \$995 \$994 \$993 \$991 \$988 \$982 \$964 \$700 \$120 \$60 \$40 \$30 \$24 \$20 \$17 Deal C \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 \$500 Err:502 ID Name 0 TreePlan 1 2 3 4 5 6 7 Value 0 Prob 0 0 0 0 Pred 0 0 0 1 1 0 2 2 Kind D E E T T T T T NS 3 2 2 0 0 0 0 0 S1 1 3 7 0 0 0 0 0 S2 2 4 6 0 0 0 0 0 S3 5 0 0 0 0 0 0 0 S4 0 0 0 0 0 0 0 0 S5 0 0 0 0 0 0 0 0 Row 13 4 14 2 7 22 17 12 Col 1 5 5 9 9 5 9 9 Mark TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Sensitivity to Value of Payoff 1 \$800 \$700 \$600 Certain Equivalent \$500 \$400 \$300 \$200 \$100 \$0 \$40 \$120 \$200 \$280 \$360 \$440 \$520 \$600 \$680 \$760 \$840 \$920 \$1,000 \$0 \$80 \$160 \$240 \$320 \$400 \$480 \$560 \$640 \$720 \$800 \$880 \$960 Payoff 1 Deal A Deal B Deal C Best Sensitivity to Proba of Drawing Red \$800 \$700 \$600 Certain Equivalent \$500 \$400 \$300 \$200 \$100 Deal A Deal B \$0 Deal C 0.03 0.09 0.15 0.21 0.27 0.33 0.39 0.45 0.51 0.57 0.63 0.69 0.75 0.81 0.87 0.93 0.99 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.78 0.84 0.90 Best 0.96 Proba of Red Ball Sensitivity to Gamma \$800 \$700 \$600 Certain Equivalent \$500 \$400 \$300 \$200 \$100 Deal A Deal B Deal C \$0 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Gamma Decision Tree for Free Clairvoyance Deal A 0.75 0.7 Red Ball 70 >>> Deal B 2 1 Deal C 0.50 0.85 \$850 Deal A 0.40 0.3 White Ball 3 0.5 >>> Deal C 0.50 0.00 Deal B 1.00 Free Clairvoyance ---> Unfold to reveal sensitivity to Proba of Red Proba of Red 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 VFC \$850 \$500 \$505 \$510 \$515 \$520 \$525 \$530 \$535 \$540 \$545 \$550 \$555 \$560 \$565 \$570 \$575 \$580 \$585 \$590 \$595 \$600 \$605 \$610 \$615 \$620 \$625 \$630 \$635 \$640 \$645 \$650 \$655 \$660 \$665 \$670 \$675 \$680 \$685 \$690 \$695 VoC \$150 \$0 \$5 \$10 \$15 \$20 \$25 \$30 \$35 \$40 \$45 \$50 \$55 \$60 \$65 \$70 \$75 \$80 \$85 \$90 \$95 \$100 \$105 \$110 \$115 \$120 \$125 \$130 \$135 \$140 \$144 \$145 \$147 \$148 \$150 \$151 \$153 \$154 \$156 \$157 \$159 \$-value \$750 u-value 0.75 \$1,000 1.00 \$500 0.50 \$400 0.40 \$0 0.00 \$500 0.50 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 \$700 \$705 \$710 \$715 \$720 \$725 \$730 \$735 \$740 \$745 \$750 \$755 \$760 \$765 \$770 \$775 \$780 \$785 \$790 \$795 \$800 \$805 \$810 \$815 \$820 \$825 \$830 \$835 \$840 \$845 \$850 \$855 \$860 \$865 \$870 \$875 \$880 \$885 \$890 \$895 \$900 \$905 \$910 \$915 \$160 \$162 \$163 \$165 \$166 \$168 \$169 \$171 \$172 \$174 \$175 \$177 \$178 \$180 \$181 \$183 \$184 \$186 \$187 \$189 \$190 \$192 \$190 \$185 \$180 \$175 \$170 \$165 \$160 \$155 \$150 \$145 \$140 \$135 \$130 \$125 \$120 \$115 \$110 \$105 \$100 \$95 \$90 \$85 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 \$920 \$925 \$930 \$935 \$940 \$945 \$950 \$955 \$960 \$965 \$970 \$975 \$980 \$985 \$990 \$995 \$1,000 \$80 \$75 \$70 \$65 \$60 \$55 \$50 \$45 \$40 \$35 \$30 \$25 \$20 \$15 \$10 \$5 \$0 ID 0 2 0 6 7 8 Name 0 TreePlan 1 2 3 4 5 6 7 8 Value 0 Prob 0 0 0 0 0 0 0 Pred Kind 0E 0D 0D 1T 1T 1T 2T 2T 2T NS 2 3 3 0 0 0 0 0 0 S1 1 3 6 0 0 0 0 0 0 S2 2 4 7 0 0 0 0 0 0 S3 0 5 8 0 0 0 0 0 0 S4 0 0 0 0 0 0 0 0 0 S5 0 0 0 0 0 0 0 0 0 Row 14 7 22 2 7 12 17 22 27 Col 1 5 5 9 9 9 9 9 9 Mark TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Sensitivity to Proba of Drawing Red \$900 \$800 \$700 \$600 Certain Equivalent \$500 \$400 \$300 \$200 \$100 Deal A Deal B \$0 0.03 0.09 0.15 0.21 0.27 0.33 0.39 0.45 0.51 0.57 0.63 0.69 0.75 0.81 0.87 0.93 0.99 Deal C 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.78 0.84 0.90 0.96 VFC Proba of Red Ball Value of Clairvoyance given Proba of Drawing Red \$160 \$140 \$120 Certain Equivalent \$100 \$80 \$60 \$40 \$20 VoC \$0 0.03 0.09 0.15 0.21 0.27 0.33 0.39 0.45 0.51 0.57 0.63 0.69 0.75 0.81 0.87 0.93 0.99 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.78 0.84 0.90 0.96 Proba of Red Ball ...
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