Eluding Game has no Saddle Point
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Theorem
The eluding game has no saddle point.
Proof
Recall the payoff table:
$\text B$ | ||
$\text A$ | $\begin{array} {r {{|}} c {{|}} c {{|}} c {{|}} } & 1 & 2 & 3 \\ \hline 1 & -1 & 1 & 1 \\ \hline 2 & 2 & -2 & 2 \\ \hline 3 & 3 & 3 & -3 \\ \hline \end{array}$ |
Trivially, by inspection, this has no entry which is the smallest entry in its row and the largest entry in its column.
Sources
- 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $3$