Eluding Game has no Saddle Point

From ProofWiki
Jump to navigation Jump to search

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