Each player has several strategies. If the first player chooses
Strategy i while the second player chooses Strategy j,
then Player 1 gains 
while Player 2 gains 
.
This outcome is represented by 
.
2-person games where the players' interests are completely opposed
are called zero-sum or constant-sum games: one player's
gain is the other player's loss. Games where the players' interests
are not completely opposed are called variable-sum games. Such
games arise in business on an everyday basis, and solving
them is not an easy task. Certain 2-person games admit pure
strategies whereas others require mixed strategies. A pure
strategy is one where, each time the players play the game, they
choose the same strategy. A mixed strategy is one where the
players introduce a random element in their choice of a strategy, thus
leaving the opponent guessing.