Maximin criterion

Maximin criterion
See also
Minimax criterion Markov model Decision table Game theory Project evaluation methods Cybernetic approach to management Book to market ratio Arrow diagram Simulation scenarios

Max-min criterion for decision making, was presented in writing on year 1950 by Abraham Wald (1902–1950). This criterion represents a pessimistic approach in decision-making (assumes the least favorable situation during taking a decision).

The max-min criterion is a decision-making approach that considers the worst-case scenario when choosing between different options. It is often used in situations where there is a high degree of uncertainty or risk involved. The criterion is based on the idea that it is better to make a decision that minimizes the maximum potential loss, rather than maximizing the potential gain.

One common application of the max-min criterion is in portfolio optimization in finance, where investors aim to minimize the maximum potential loss of their portfolio while maximizing its potential return. The criterion can also be used in project management, where decision makers aim to minimize the negative impact of potential risks on the project's success. In operations research, it is applied to select the best action or strategy to minimize the maximum possible loss or regret.

In summary, max-min criterion is used to minimize the maximum potential loss, in situations where there is high degree of uncertainty or risk involved, in fields like finance, project management, and operations research.

Application

According to the max-min criterion first for each strategy of payoff matrix, we should determine the minimum value. And then choose the strategy, for which the minimum payout, is the largest.

$v={\underset {i}{max}}\{{\underset {j}{min}}\{a_{ij}\}\}$

Example

Example: we have an array of payments from the four possible decisions and three possible states:

${\underset {Strategies}{}}\diagdown {\overset {States\ of\ nature}{}}$	I	II	III
T1	200	100	120
T2	0	300	−200
T3	0	300	500
T4	−100	200	0

We are looking for a minimum winnings for each strategy, and then select the largest:

Strategies	${\underset {j}{min}}\{a_{ij}\}$
T1	100
T2	−200
T3	0
T4	−100

Summing up: According to the Max-min criterion manager should choose a strategy T1.

References

• Hassan, N., Siew, L. W., & Shen, S. Y. (2012). Portfolio decision analysis with maximin criterion in the Malaysian stock market. Applied Mathematical Sciences, 6(110), 5483-5486.