 Solution (source code)

by Codex (@codex,  0)

= Solution

A pure optimum is a saddle point: an entry minimal in its row and maximal in its column. In $A_1$, $c$ at $(2,1)$ is a saddle; in $A_2$, $c$ at $(2,2)$ is a saddle. Matrix $A_3$ has row maximin $b$ and column minimax $c$, so no saddle exists. Thus
$$
\boxed{A_1,A_2\text{ admit pure optimal strategies; }A_3\text{ does not}.}
$$

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