Decision Theory: Maximin and Minimax strategy

Maximin and Minimax strategy

Maximin criteria

This criterion is the decision to take the course of action which maximizes the minimum possible pay-off. Since this decision criterion locates the alternative strategy that has the least possible loss, it is also known as a pessimistic decision criterion. The working method is:

(i) Determine the lowest outcome for each alternative.

(ii) Choose the alternative associated with the maximum of these.

Minimax criteria

This criterion is the decision to take the course of action which minimizes the maximum possible pay-off. Since this decision criterion locates the alternative strategy that has the greatest possible gain. The working method is:

(i) Determine the highest outcome for each alternative.

(ii) Choose the alternative associated with the minimum of these.

Example 10.10

Consider the following pay-off (profit) matrix Action States

Determine best action using maximin principle.

Solution:

Example 10.11

A business man has three alternatives open to him each of which can be followed by any of the four possible events. The conditional pay offs for each action - event combination are given below:

Determine which alternative should the businessman choose, if he adopts the maximin principle.

Solution:

Max (–10,–4, 0) = 0. Since the maximum payoff is 0, the alternative Z is selected by the businessman.

Example 10.12

Consider the following pay-off matrix

Using minmax principle, determine the best alternative.

Solution:

min( 27, 25, 23, 32) = 23. Since the minimum cost is 23, the best alternative is E3 according to minimax principle.