A situation in which one participant's gains result only from another participant's equivalent losses. The net change in total wealth among participants is zero; the wealth is just shifted from one to another.
Options and future contracts are examples of zero-sum games . For every person who gains on a contract, there is a counter-party who loses. Gambling is also an example of a zero-sum game.
A stock market, however, is not a zero-sum game because wealth can be created in a stock market.