Zero-sum game

A zero-sum game is a term in game theory and economic theory. 
It is a mathematical representation of a situation. Each individual's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will add up to zero. So, cutting a cake is a zero-sum game. 
Not so obvious, but essential, is "how players (participants) value the cake". A zero-sum game exists if and only if all players value the cake equally (see marginal utility).