Game Saddle Point

For a general two-player zero-sum game,


If the two are equal, then write


where v is called the value of the game. In this case, there exist optimal strategies for the first and second players.

A necessary and sufficient condition for a saddle point to exist is the presence of a payoff matrix element 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

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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.

Referenced on Wolfram|Alpha

Game Saddle Point

Cite this as:

Weisstein, Eric W. "Game Saddle Point." From MathWorld--A Wolfram Web Resource.

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