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
© 1996-9 Eric W. Weisstein
1999-05-25