Define the terms 'state of nature' and 'course of action' as used in decision theory, and illustrate both usin

Exercises · Q12

Q. Define the terms 'state of nature' and 'course of action' as used in decision theory, and illustrate both using the payoff table of Worked Example 6.

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A course of action (also called an alternative or strategy) is one of the choices actually available to and controlled by the decision-maker — in Worked Example 6, $A_1, A_2, A_3$ represent the firm's own decision of which course of action to adopt (for example, which scale of investment or which product line to launch).

A state of nature is a condition of the external environment that will actually occur in the future, but which the decision-maker cannot control or influence — in Worked Example 6, $S_1, S_2, S_3$ represent different possible market/demand conditions that could arise regardless of which action the firm takes. …

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

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

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Q.Define the terms 'state of nature' and 'course of action' as used in decision theory, and illustrate both using the payoff table of Worked Example 6.

Concept understanding — Decision-Making under Uncertainty

Q.Define the terms 'state of nature' and 'course of action' as used in decision theory, and illustrate both using the payoff table of Worked Example 6.

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