# EVPI

Topics: Decision theory, Decision tree, Game theory Pages: 9 (687 words) Published: January 26, 2015
Expected Value of Perfect
Information (EVPI)

In decision-making under risk , each state of nature is associated with probability of its occurrence ;
If the decision-maker can acquire perfect (complete) information about the occurrence of various states of nature , he will be able to select a strategy that yields the desired pay-off for whatever state of nature that actually occurs

EMV /EOL criterion helps the decision-maker select a strategy that optimises the expected pay-off without complete information EVPI =Expected profit with perfect information-expected profit without complete information

=Expected loss without complete information-Expected
loss with perfect information.

Decision Tree

Is a technique for handling multi-stage decision
problem, where consequence of one decision affects
future decisions
This analysis involves construction of a diagram
showing all the strategies , states of nature and
probabilities associated with the states of nature
A decision tree consists of nodes , branches
,probability estimates and pay-offs.
Nodes are of two types : decision nodes and chance
nodes

Decision Tree

A decision node is usually represented by a square ,
where a decision-maker must make a decision
Each branch leading away from a decision node
represents one of the strategies available to the DM
A chance node is usually represented by a circle and
indicates a point where the DM will discover the
response to his decision, i.e., different possible
outcomes from a chosen course of action

Decision Tree

Branches emanate from and connects various nodes
( decision/ states of nature)
Two types of Branches : decision branches & chance
branches
Decision Branch: Each branch leading away from
the decision node represents a strategy that can be
chosen at a decision point
Chance Branch : A branch leading away from the
chance node represents the states of nature of a set of
chance factors .Associated probabilities are indicated
alongside of respective chance branch

Decision Tree

Terminal Branch :Any branch that makes the
end of the decision tree , i.e., it is not followed
by either a decision or chance node
Pay-offs : can be positive (revenue/sales ) or
negative ( expenditure/cost ) and they can be
associated either with a decision/chance
branch

Operation in a Decision Tree

The optimal sequence of decision is found by
starting at the right hand side and rolling
backward
The aim of this operation is to maximise the
return from the decision situation
At each node , the expected return (Position
value ) should be calculated

Operation in Tree

If the node is a chance node , the position value is calculated as the sum of the products of the probabilities of the branches emanating from the chance node and their respective position values
If the node is a decision node , the expected return is
calculated for each of its branches and the highest return is selected
The procedure continues until the initial node is reached
The position value for initial node corresponds to the
maximum expected return obtainable from the decision
sequence

Illustration
A manufacturer of toys is interested to know whether he should launch a deluxe model or a popular model of the toy . If the deluxe model is launched, the probabilities that the market will be good , fair or poor are given by 0.4,0.3 and 0.3 respectively with pay-offs of Rs. 1,80,000/- , Rs. 1,00,000/- and Rs.20,000/- respectively. If the popular model is introduced , the corresponding probabilities are given by 0.3,0.4 and 0.3 with respective pay-offs of Rs. 2,00,000/- Rs. 1,50,000/- and Rs. 20,000/-. The problem is to decide which model should be

launched ?

Problem-1
A person has two independent investments A & B available
to him ;but he undertakes only one at a time due to certain
constraints...