Let the elements in a Payoff Matrix be denoted , where the s are player A's Strategies
and the s are player B's Strategies. Player A can get at least

(1) 
for Strategy . Player B can force player A to get no more than
for a Strategy . The
best Strategy for player A is therefore

(2) 
and the best Strategy for player B is

(3) 
In general,

(4) 
Equality holds only if a Saddle Point is present, in which case the quantity is called
the Value of the game.
See also Game, Payoff Matrix, Saddle Point (Game), Strategy, Value
© 19969 Eric W. Weisstein
19990525