Question

Payoffs for the following acts depend on the roll of a die. Consider the following decision table.

1 2 3 4 5 6

A 100 200 300 400 500 600

B 600 200 500 200 200 200

C 700 500 400 400 200 100

For example, if the roll is "1", then you win $100 if you choose A, $600 if you choose B, and $700 if you choose C.

a) Using EMV, what should you choose? b) What is the most you would pay for perfect information on the die roll?

Answer 1

here as probability of a number on die =1/6

a)

expected value of A =(100+200+300+400+500+600)/6=350

expected value of B =(600+200+500+200+200+200)/6=316.67

expected value of C =(700+500+400+400+200+100)/6=383.33

hence EMV =max(expected value of A,B,C) =max(350 ,316.67 ; 383.33)=383.33

hence one should choose C

b)

here expected value with perfect information

=(700+500+500+400+500+600)/6=533.33

hence most one should pay =expected value with perfect information-EMV

=533.33-383.33=150