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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