Definition
A zero-sum game is a situation where everyone's gains and losses add up to exactly zero. The total reward is fixed, so if someone gains, someone else has to lose the same amount. That makes it a tough, head-to-head kind of competition.
The size of the pizza is fixed
Picture a table with two people and one pizza cut into exactly eight slices. The size of the whole pizza is already set. If I get greedy and eat five slices, my friend, like it or not, only gets three.
Compare that with splitting it fairly at four slices each. The one extra slice I gained (+1) matches the one slice my friend lost (-1) exactly. Add up the gains and losses and you get zero. When the thing being divided has a fixed size, one person's gain is another person's loss.
Sports, card games, and chess are the easiest examples. Only one person can wear the gold medal, and the winner's joy is matched by the loser's disappointment. In a gambling game where the organizer takes no cut, the money one player wins comes straight out of another player's pocket.
The economy is often not zero-sum
Many people think trade in markets, or trade between countries, is a dog-eat-dog zero-sum game where one side wins and the other gets fleeced. But real economic activity is closer to a process of making the pizza itself bigger and bigger.
Say a farmer who bakes amazing bread meets a tailor who makes great clothes. Each focuses on what they do best, then they trade fairly at the market. Both end up much better fed and warmer than before. A voluntary trade like this can make both sides better off without taking anything from anyone.
To be more precise, the modern economy as a whole is closer to a positive-sum game that grows the whole pie. Advances in technology and smarter use of resources keep creating new value. But even when the pie grows, not everyone's share grows along with it. On the flip side, a situation like war, where the gains and losses add up to a net loss, is called a negative-sum game.
The trap of zero-sum thinking
Of course, there are still plenty of zero-sum contests around us. Admission to a top university with limited seats, or the single executive promotion slot at a company, is a cold reality: if someone gets in, someone else has to miss out.
But treating every relationship and every business deal as zero-sum is very risky. This "zero-sum mindset" makes you mistake a coworker's success for your own failure, and pulls you into pointless backbiting and jealousy.
Smart people don't fight over a slice of someone else's pie. They first think about how to work together and grow the whole market. So before jumping into any competition, figuring out what kind of situation you're in is the starting point of good decision-making.
Common misconceptions
All economic activity and free trade are zero-sum games.
Free exchange and technological progress are positive-sum: they grow the whole pie (total output). They can be a win-win for everyone, but the extra gains aren't always shared evenly.
Where you meet it
A chess match, where one player's win means the other's loss (in a draw, neither side gains or loses anything).
Gambling among players where the organizer takes no cut (at a real casino, once fees come in, it becomes negative-sum for the players as a group), or futures and options trading, where, fees aside, one side's profit equals the other side's loss.
In one sentence
A zero-sum game is one where one side's gain exactly matches the other side's loss, so the total comes out to zero.