A decision tree is a graphic device that shows a sequence of strategic
decisions and the expected consequences under each possible set of
The construction and analysis of a decision tree is
appropriate whenever a sequential series of conditional decisions
must be made under conditions of risk.
By conditional decision, we mean a decision that depends upon circumstances or options that will occur at a later time.
Construction of the decision tree
Construction of the decision tree begins with the first or earliest decision and proceeds forward in time through a series of subsequent events and decisions.
At each decision or event the tree branches out to show each possible course of action, until finally all logical consequences and the resulting payoffs are depicted.
The exhibit describes a problem faced by a firm that must decide whether a firm must decide whether to speed Rs 350,000 to market a new product or to invest the money elsewhere for a 10% per annum return.
Taking the sequence of events from left to right, the first decision (symbolized by a square is whether or not to market the product. If the product isn’t marketed, the payoff will be Rs 35,000 from the alternative investment.
If the firm markets the product, the next event (a non-controllable situation, symbolized by a large circle) may be the entry of a competitor into the market. The probability of competition (0.8) and the probability of no competition (0.20) are in parentheses beside the appropriate branches.
Importance of Decision Tree
It is important to note that in the construction of a decision tree, the branches out of squares represent strategies and the branches out of large circles represent states of nature.
Since the decision-maker has full control over which strategy is chosen, the branches out of squares do not have probabilities. But the decision-maker has no control over states of nature.
Therefore, the branches out of large circles have probabilities and the probabilities for all branches coming from anyone circle must add up to 1.0. In this example, the probabilities of competition (0.80) and no completion (0.20) add up to 1.0, since one or the other must happen.
If there is no competition the only remaining decision is whether to charge a high, medium or low price. The three branches are drawn and labelled (high medium, low) and the payoff for each is noted at the end of each branch. If there is competition, the same three branches are appropriate.
However, each branch divides again to reflect the competitor’s options to price high medium or low. The competitor’s options are states of nature, so they proceed out of a circle.
Branches of Decision Tree
Each of these final branches is marked with a probability and the payoff is noted at the end of each one once again, the probabilities add up to 1.0 for each circle, since the competitor is certain to charge either a high, medium or low price.
The decision tree thus depicts in graphic form the expectation that the price a competitor charge depends upon the price the firm sets.
At the same time, the fire’s consequent profits depend upon what price the competitor charges.
Since each decision depends upon the evaluation of events taking place at a later time, the analysis of a decision tree begins at the end of the sequence and works backwards.