Saddle Point (Game)
For a general two-player Zero-Sum Game,
If the two are equal, then write
where
is called the Value of the Game. In this case, there exist optimal strategies for the first andsecond players.A Necessary and Sufficient condition for a saddle point to exist is the presence of a Payoff Matrixelement which is both a minimum of its row and a maximum of its column. A Game may have more than one saddle point,but all must have the same Value.
See also Game, Payoff Matrix, Value
References
Dresher, M. ``Saddle Points.'' §1.5 in The Mathematics of Games of Strategy: Theory and Applications. New York: Dover, pp. 12-14, 1981. Llewellyn, D. C.; Tovey, C.; and Trick, M. ``Finding Saddlepoints of Two-Person, Zero Sum Games.'' Amer. Math. Monthly 95, 912-918, 1988.
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