Unformatted text preview: worth to Liedtke? 41 Taking ulies into account Original Decision Tree EU Analysis • U(x) = 1 exp( x/R), R=1 • U(0) = 0 • U(2) = 0.865 • U(3) = 0.950 • U(5) = 0.993 • U(10.3) = 1 EU(counteroﬀer) = (.17)(0.993) + (0.5)(0.697) + (0.33)(0.950) = 0.8308 CE(counteroﬀer) =  ln(1 0.8308) = $1.777 Bn => Leidtke should accept $2 Bn oﬀer 42 With Informaon • Take 5 Bn if Texaco accepts • Take 2 Bn if Texaco refuses • Take 3 Bn if Texaco counteroﬀers • EU(Info) = (0.17)
(0.993)+ (0.5)
(0.865) + (0.33)
(0.950) = 0.9148 • => CE(Info) = $2.463 Bn 43 T P One More Time  Cont’d. • Assuming that C = 0, the certainty equivalent for the informaon branch is about $2.463 Bn. • EVPI thus would be $2.463 Bn  $2.00 Bn = $463 million • Liedtke should spend no more than $0.46 billion on informaon about Texaco’s response. If the informaon were to cost more, Liedtke would be beeer oﬀ simply accepng the $2 billion counteroﬀer. 44 Value of Informaon • Problems involving value of informaon calculaons can quickly become complicated • Example – Problem 12.14, p. 557 45 Problem 12.14  a EVPI of weather informaon = 13.75 – 11.25 = 2.5K = $2,500 Clearly, the farmer beneﬁts from knowing the weather 46 Problem 12.14  b • Let X = loss if burners are used and freeze occurs and Y= loss if sprinklers are used and freeze occurs • Expected loss with informaon = E[min(5 + ½ X, 2 + ½ Y)] • This is diﬃcult to calculate • Use Extended Pearson Tukey 3 point approximaon • Procedure: calculate x.05, x.5, x.95, y.05, y.5, y.95. Assign probabilies 0.185 to the 5th and 95th percenles and probability 0.63 to the median • Calculate expected loss with informaon • Calculate EVPI = 13.5K – 13.741K = $9 • The farmer b...
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 Spring '08
 Gupta,D
 Game Theory, Pennzoil, Expected value of perfect information

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