What defines a two-person, zero-sum game?

A two-person, zero-sum game is defined by the principle that one player's gain is exactly equal to the other's loss. This creates a situation where the total benefit to all players remains constant, which is typically expressed as zero; hence, if one player increases their score or payoff, the other player must have an equivalent decrease in theirs. This characteristic captures the essence of competitive scenarios where the interests of the two players are directly opposed, fundamentally distinguishing this type of game from cooperative ones where players may achieve mutual benefits.

For example, in a zero-sum game, if Player A wins 10 points, Player B would simultaneously lose 10 points, resulting in a net change of zero. This clear contrast in payoffs underlies many strategic decision-making scenarios such as games of chess or poker, where the success of one competitor inherently comes at the expense of another.