Decision Trees
DECISION TREES
DECISION
Decision trees may be described as the graphic display of the decision-making process. Let us take for example a situation where one must decide whether to go to a movie house or to stay at home and watch TV or a video tape.
State of nature node Branches Good movie
Decision node
Movies Bad Movie
Good program TV New program or cassette Poor program Rerun Good program
Poor program
The square node signifies a decision point; each alternative is followed by a circular node from which branches on the tree represent the possible outcomes or states of nature which could result.
Strictly speaking, a decision tree must contain both probabilities of outcomes and conditional monetary values of those outcomes so that expected values can be computed.
Let us apply the decision tree in an investment problem. Suppose we are to decide whether to invest our $1000 in stocks or to deposit it in our savings account. Let us further assume that our savings account will not be affected by the performance of the stock market and that it pays an annual interest of 5%. If the market rises, the value of our investment in stock will become $1,400; if the market falls, our investment’s value will decrease to $800. There is a 0.7 probability that the market will rise and a 0.3 probability that the market will fall.
Our decision tree analysis follows:
1 Market rises 0.7 x $1,400
DECISION
Stocks
M Market falls 0.3 x $800
2
Market rises 0.7 x $1,050 Savings account Market falls 0.3 x $1,050
The procedure in analyzing a decision tree is to work backward through the tree (from right to left), computing the expected value of each state of nature node. We then choose the particular branch leaving the decision node which leads to the state of nature node with the highest expected
DECISION
Decision trees may be described as the graphic display of the decision-making process. Let us take for example a situation where one must decide whether to go to a movie house or to stay at home and watch TV or a video tape.
State of nature node Branches Good movie
Decision node
Movies Bad Movie
Good program TV New program or cassette Poor program Rerun Good program
Poor program
The square node signifies a decision point; each alternative is followed by a circular node from which branches on the tree represent the possible outcomes or states of nature which could result.
Strictly speaking, a decision tree must contain both probabilities of outcomes and conditional monetary values of those outcomes so that expected values can be computed.
Let us apply the decision tree in an investment problem. Suppose we are to decide whether to invest our $1000 in stocks or to deposit it in our savings account. Let us further assume that our savings account will not be affected by the performance of the stock market and that it pays an annual interest of 5%. If the market rises, the value of our investment in stock will become $1,400; if the market falls, our investment’s value will decrease to $800. There is a 0.7 probability that the market will rise and a 0.3 probability that the market will fall.
Our decision tree analysis follows:
1 Market rises 0.7 x $1,400
DECISION
Stocks
M Market falls 0.3 x $800
2
Market rises 0.7 x $1,050 Savings account Market falls 0.3 x $1,050
The procedure in analyzing a decision tree is to work backward through the tree (from right to left), computing the expected value of each state of nature node. We then choose the particular branch leaving the decision node which leads to the state of nature node with the highest expected