# zero-sum game

In game theory, a zero-sum game is a game in which a win for one player results in an equal but opposite loss for the other players. The theory of zero-sum games is very different from that of non-zero-sum games because an optimal solution can always be found.

In a two-person zero-sum game, the payoff to one player is the negative of that to the other. Many common card and board games, such as poker and chess are zero sum: one player wins, another loses. According to von Neumann's theory of games, every zero sum game has a value. Each player can guarantee himself or herself this value against any play of an opponent, and can prevent the other player from doing any better than this. The outcomes of a two-player zero-sum game can be shown in the form of a matrix in which one player corresponds to the rows and the other the columns. The entries in the matrix are the payoffs to the row player.