With the probabilities of the states of nature unknown, each of the four classical criteria looks at the same payoff table from a different attitude to risk — optimistic, pessimistic, regret-minimising, or equal-likelihood — and they need not agree on the same action. …

1. Maximax (optimist): row maxima are $A_1=200$, $A_2=300$, $A_3=400$. The highest row maximum is 400 → recommends $A_3$.
2. Maximin (Wald, pessimist): row minima are $A_1=200$, $A_2=100$, $A_3=50$. The highest row minimum is 200 → recommends $A_1$.
3. Minimax Regret (Savage): build the regret table by subtracting each payoff from its column's best payoff. Column bests: $S_1=200$, $S_2=300$, $S_3=400$.

The smallest of the row maximum regrets is $\min(200,100,150)=100$ → recommends $A_2$.

(d) Laplace (equal probability): average payoff per action, each state weighted $1/3$:

$\bar A_1=\frac{200+200+200}{3}=200,\quad \bar A_2=\frac{100+300+300}{3}=233.33,\quad \bar A_3=\frac{50+200+400}{3}=216.67$ …

Cross-check the regret table by re-scanning each column a second time for its true maximum before subtracting — an error in a single column ma …

Applying the Maximax rule to the regret table instead of the payoff table (regret should always be minimised, since it measures how far short of the best possible outcome an action falls, never maximised); and buildin …