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).

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.