Lecture 13 - Utility & Information

Lecture 13 - Utility & Information - Lecture 13...

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1 Lecture 13 Decision Analysis with Utility The Value of Information
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2 Administrative Details Homework 6 is due a week from  Thursday Questions from last class? Midterm Thursday
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3 Utility and Information Values Using certainty equivalents (CE) to measure the value  of information with utility What does purchasing information do? Changes the nature of uncertainty Reduces the final payouts by the cost of the information Converting uncertainty into certainty can be costly – is the cost  justified? In “expected value world,” it didn’t matter when or  how we removed the cost of the information from the  problem In “expected  utility  world,” the cost needs to be passed  through the utility function
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4 The Party Problem with Utility Outdoors Indoors Sun Rain Sun Rain 200 0 120 100 0.6 0.4 0.6 0.4 -0.481 -0.328 EU = -0.328 Wealth u(Wealth) -0.135 -1.000 -0.301 -0.368 u( x ) = - e - α x α  = 0.01 Always maximize utility!
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5 The CE of the Party Problem ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 51 . 111 $ 328 . 0 ln 01 . 0 1 ln 1 ln 328 . 0 = - - - = = - - - = - - = - = - x x x u x x u e x u EU x α CE =  x
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6 Utility and Perfect Information Suppose we wish to acquire perfect information Where we account for the cost of it matters a great deal -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 $0 $25 $50 $75 $100 $125 $150 $175 $200 x u(x) $25 matters a lot here $25 doesn't matter so much here
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7 Utility and Perfect Information Outdoors Indoors Sun Rain 200 –  c 120 –  c 0 –  c 100 –  c 0.6 0.4 u (200 –  c ) u (100 –  c ) EU = 0.6 × u (200 –  c ) + 0.4 ×  u (100 –  c ) Wealth u (Wealth) -e - α (200- c ) u ( x ) = - e - α x α  = 0.01 Reflect information costs in final wealth Outdoors Indoors -e - α (120- c ) -e - α (100- c ) -e - α (- c )
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8 Utility and Perfect Information EU(No Information) = -0.328 EU(Perfect Information) = 0.6 × u (200 –  c ) + 0.4 ×  u (100 –  c ) Determine the maximum value (cost) of perfect information as the  breakeven point ( 29 ( 29 ( 29 [ ] ( 29 [ ] ( 29 17 . 36 $ 4386 . 1 ln 01 . 0 4386 . 1 328 . 0 228 . 0 328 . 0 4 . 0 6 . 0 328 . 0 100 4 . 0 200 6 . 0 01 . 0 01 . 0 100 01 . 0 200 01 . 0 = = = - = - - = - + - - = - + - - - - - c c e e e e c u c u c c c c Quadratic utility and multiple roots?
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9 Utility and Perfect Information The decision maker with  that  particular utility  function would be willing to pay  up to  $36.17  for perfect information Note: For the special case of exponential utility,  the EVPI = CE(EUPI) – CE(EUNI) CE(EUPI) = $147.69 CE(EUNI) = $111.51 (calculated earlier) Therefore EVPI = $36.17 (within rounding)
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10 Expected Utility and Information Cost -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0 10 20 30 40 50 Cost  of I nformat ion Utility EU(Buy) EU(Don't) Breakeven Cost of Information =  $36.17
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Lecture 13 - Utility & Information - Lecture 13...

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