# decision analysis with examples

Written by Dinesh Thakur

In decision-making under risk, the probabilities of various states of nature are assumed to be known. Probabilities of the various states of nature are not known to the decision–maker and thus, he cannot apply the maximization/minimization of expected value criteria as in the case of decision under risk.

In such a decision problem, the following decision rules/criteria, depending upon the attitude of the decision maker, may be applied.

i)                    Maximax rule or criterion of optimism.

ii)                   Maximin rule or criterion of pessimism.

iii)                 Criterion of minimize regret, and

iv)                Criterion of rationality

i)        Maximax or Criterion of Optimism

In this case, the decision-maker is of optimistic attitude and thus would select the strategy, which will provide him the greatest (max) pay-off under the most favorable or the best condition (max). In the above example, the decision-maker will select strategy S2 which will give him a maximum pay-off Rs.10 lakh for launching a new PC and for the same condition.

 Strategies States of nature Same condition New Competitor Govt. Ban (S1)  Modify 7 5 -5 (S2) New product 10 3 -13 (S3)   Do nothing 5 1 -2

Strategy                                  Maximum or the best pay-off

S1                                                        7

S2                                                        10 ß maximum pay-off

S3                                                        5

ii) Maximin or Criterion of Pessimism

As the name of the criterion indicates, the decision maker is of pessimistic attitude and thus will select the strategy which will give him the highest pay-off (max) if the worst condition (min) occurs. Here, the decision–maker, being of pessimistic view, will not like to take any risk and thus will think about the safest position in the worst situation, Thus, the decision-maker will select strategy S3 since in the worst situation (government ban) he will sustain the minimum loss (Rs. 2 lakh) due to this decision.

Strategy                                  worst or the minimum pay-off

S1                                                        -5

S2                                                        -13

S3                                                        -2ß minimum pay-off