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Decision Theory

Decision theory may be defined as a sat of general concepts and techniques that assist a decision maker in choosing among alternatives. Decision theory problems are commonly cast in a standard framework, termed as a decision matrix which consists of the following components.
                                                             DECISION MATRIX
                               States of nature (N) and Probabilities of Occurrence (Pr)
                                          N1           N              N3             -               Nn
Strategies (s)
                                         Pr1         Pr2              Pr3             -              Prn

S1                                   O11           O12              O13           -            O1n

S2                                   O21           O22              O23             -           O2n

Sm                                 Om1          Om2              Om3             -          Omn
(a)    Strategies or alternatives (S), available to the decision market. For example, make or buy would be two strategies in a make- or buy decision problem. Strategies are within control of the decision maker.
(b)    States of Nature (N) , which are characteristics of the environment and are beyond the control of decision maker. The term derives from the weather, where we might say, three is termed one of certainty.

If the decision maker can assign probability of occurrence to one or more states of natures with no one state given a value of 1.0, It is termed as risk situation.

Finally, if the decision maker has no idea of the probabilities of occurrence of any state of nature, the situation is defined as decision making under uncertainty.

Thus in the decision matrix above, there whole be an entry for probability if the situation is one of certainty or risk and no entry if it is one of uncertainty.
(c)    Pay offs or outcomes (O) , which represent the value associated with each combination of strategy and state of nature. The value may be stated in terms of utility, cost profit satisfaction etc.

Solving a decision theory problem obviously requires some choice to be made form among the alternatives, antes some rule or decision criterion must be selected for this purpose. For e.g., in certainty situations, the decision criterion is to select the single strategy with the highest pay off. Since only one state of nature is relevant, this entails a simple scanning of the pay off column under the certain N and picking the best one.

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