We consult a patent attorney on our chances of being awarded a patent, he gives

Question

We consult a patent attorney on our chances of being awarded a patent, he gives us the following evaluation of his performance in terms of conditional probabilities.

Patent Awarded

Patent Not Awarded

“Patent Award”

0.75

0.10

“No Patent Award”

0.25

0.90

What is the maximum amount you would pay for his services? Draw the decision tree.

Patent Awarded

Patent Not Awarded

“Patent Award”

0.75

0.10

“No Patent Award”

0.25

0.90

00 Verizon 11:29 AM Today 11:26 AM Edit License Technology 23 25 Demand High (0.25) Patent Award (0.7) 43 10 Continue Development Develop Marketing& Production Demand Mediunm (0.55) 21 -2 Demand Low (0.20) Patent Award (0.3) Stay Development -2

Explanation / Answer

In the given diagram of decision tree, once Patent is awarded, there are two alternate actions 1 licence technology having net value 23 and 2. Developing, marketing & production having three states of Demand (high, medium and low) with net values 43, 21 & 3 with probabilities .25, .55 & .20 respectively. So expected net value is calculated as 22.9 (.25*43+.55*21+.2*3)

Therefore the best option in case Patent Awarded is License Technology with net value of 23, given probability of this state is .7

In the state of No Patent Awarded net value is -2, given probability of this state is .3

Expected Value in the absence of consulting attorney = 15.5 (.7*23+.3*(-2))

Expected value under perfect information = 17.25

Maximum amount that can be paid = 1.75

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