Given the following pay-off matrix (in rupees) for three strategies and two states of nature. | Strategy | $E_1$ | $E_2$ | | --- | --- | --- | | $S_1$ | 40 | 60 | | $S_2$ | 10 | $-20$ | | $S_3$ | $-40$ | 150 | Select a strategy using each of the following rule : (i) Maximin (ii) Minimax

> > [!TLDR] > Maximin selects $S_1$ (best of the worst payoffs); the minimax-regret rule selects $S_3$ (smallest of the maximum regrets). > > In the TN HSC Class-12 Business Maths decision-theory topic, these criteria are used when the probabilities of the states of nature are unknown (decision-making under uncertainty). > > **Pay-off matrix (₹):** > > | Strategy | $E_1$ | $E_2$ | Row min | > | --- | --- | --- | --- | > | $S_1$ | 40 | 60 | 40 | > | $S_2$ | 10 | $-20$ | $-20$ | > | $S_3$ | $-40$ | 150 | $-40$ | > > **(i) Maximin criterion.** Choose the strategy whose **minimum** payoff is the **largest**. > Row minimums are $40,\ -20,\ -40$; the maximum of these is $40$. > $$\Rightarrow \text{Select } S_1.$$ > > **(ii) Minimax (regret) criterion.** First build the regret (opportunity-loss) matrix: for each state subtract every payoff from the best payoff in that column. > > - Column $E_1$: best $=40$ $\Rightarrow$ regrets $S_1{:}\,0,\ S_2{:}\,30,\ S_3{:}\,80$. …

Given the following pay-off matrix (in rupees) for – Class 12 Business Mathematics Statistics

Question 30 of 38

Given the following pay-off matrix (in rupees) for three strategies and two states of nature.

Strategy	$E_1$	$E_2$
$S_1$	40	60
$S_2$	10	$-20$
$S_3$	$-40$	150

Select a strategy using each of the following rule :

Maximin
Minimax

Tamil Nadu DgeTamil Nadu HSC (DGE) Commerce Board 2024Subjective· 3mImportance★★★★★

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Maximin selects $S_1$ (best of the worst payoffs); the minimax-regret rule selects $S_3$ (smallest of the maximum regrets).

In the TN HSC Class-12 Business Maths decision-theory topic, these criteria are used when the probabilities of the states of nature are unknown (decision-making under uncertainty).

Pay-off matrix (₹):

Strategy	$E_1$	$E_2$	Row min
$S_1$	40	60	40
$S_2$	10	$-20$	$-20$
$S_3$	$-40$	150	$-40$

Maximin criterion. Choose the strategy whose minimum payoff is the largest. Row minimums are $40,\ -20,\ -40$ ; the maximum of these is $40$ . $\Rightarrow \text{Select } S_1.$
Minimax (regret) criterion. First build the regret (opportunity-loss) matrix: for each state subtract every payoff from the best payoff in that column.

Column $E_1$ : best $=40$ $\Rightarrow$ regrets $S_1{:}\,0,\ S_2{:}\,30,\ S_3{:}\,80$ . …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH2 marks
$S_1$
›Reveal solutionSolution

Take the smallest pay-off in each row, then pick the row with the largest such minimum: that is $A_4$ with value $15$ .

The maximin criterion is used for decision-making under uncertainty by a cautious (pessimistic) decision-maker who guards against the worst outcome of each action.

Step 1 — Minimum pay-off (worst state) for each action:

Action $S_1$ $S_2$ $S_3$ $S_4$ Row minimum
$A_1$ 5 10 18 25 5
$A_2$ 8 7 8 23 7

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CBSE 2020Set MARCH2 marks
$E_1$
(i) Maximin
(ii) Minimax
›Reveal solutionSolution
Maximin selects the best of the row minima ( $S_1$ ); Minimax regret selects the strategy whose largest regret is smallest ( $S_3$ ).

Pay-off matrix (rupees):

Strategy $E_1$ $E_2$ Row min
$S_1$ 40 60 40
$S_2$ 10 $-20$ $-20$
$S_3$ $-40$ 150 $-40$

Maximin criterion (pessimistic — best of the worst pay-offs). Take each row's minimum, then the maximum of those minima: $\max\{40,\ -20,\ -40\} = 40 \ \Rightarrow\ \textbf{Strategy } S_1.$

Minimax (regret) criterion (Savage). Build the regret (opportunity-loss) table: in each state, regret $=$ (best pay-off in that column) $-$ (pay-off). Column maxima are $E_1 = 40$ , $E_2 = 150$ .

Strategy $E_1$ regret $E_2$ regret Max regret
$S_1$ $40-40=0$ $150-60=90$ 90
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Action	$S_1$	$S_2$	$S_3$	$S_4$
$A_1$	5	10	18	25
$A_2$	8	7	8	23
$A_3$	21	18	12	21
$A_4$	30	22	19	15

Action	$S_1$	$S_2$	$S_3$	$S_4$	Row minimum
$A_1$	5	10	18	25	5
$A_2$	8	7	8	23	7

Strategy	$E_1$ (States-of-nature)	$E_2$ (States-of-nature)
$S_1$	$40$	$60$
$S_2$	$10$	$-20$
$S_3$	$-40$	$150$

Strategy	$E_1$ regret	$E_2$ regret	Max regret
$S_1$	$40-40=0$	$150-60=90$	90

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