A zero sum game, is one where the net change to all players, is zero. Total gains experienced by players in zero sum game is equal to total losses experienced by other players. The number of players in zero sum game can vary from as little as two up to as many as several million.
A hypothetical example:
Imagine two friends, Roger and Raphie, are watching a tennis match between Federer and Nadal. Roger says 'I bet you $10 that Federer will win'. Raphie agrees. The possible payouts of this bet are shown below:
In investment markets, options and futures are both zero sum games. (if you ignore brokerage fees). They are markets where money is not made or lost, it just changes hands.