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 game saddle point is present, in which case the quantity is called the value of the game.
