What Is a Zero-Sum Game? Meaning and Examples
Quick answer
A zero-sum game is a situation where one participant can only gain if another loses the same amount, so the total for everyone always adds up to zero. Poker and betting are the classic examples. The opposite is a non-zero-sum game, which is either positive-sum (the total can grow) or negative-sum (it shrinks).
Zero-sum vs non-zero-sum games compared
| Game type | Sum of all gains and losses | What it means | Examples |
|---|---|---|---|
| Zero-sum | Always zero | One side gains exactly what the other side loses; no new value is created | Poker, betting, dividing a fixed inheritance, a penalty shootout, one buyer outbidding another for a fixed asset |
| Positive-sum (non-zero-sum) | Can grow | Everyone involved can end up better off at once because new value is created | A voluntary trade, economic growth, a low-cost global index fund held for decades |
| Negative-sum (non-zero-sum) | Shrinks | The participants as a group end up with less than they started, even if some individuals win | Poker after the house takes its rake, active trading after fees, a price war, litigation, war |
| Constant-sum | Fixed but not necessarily zero | The total is fixed, so more for one means less for another; strategically the same as zero-sum | Splitting a fixed pot of prize money between players |
A zero-sum game is a term from game theory for any situation where one person's gain is exactly matched by another person's loss, so no matter who wins, the total for everyone stays the same. The name comes from the arithmetic: add up all the gains and losses and they cancel to zero. Poker is the textbook case, because no wealth is created at the table; the chips just change hands.
The table above sets zero-sum games against their opposite, the non-zero-sum game, which splits into positive-sum (where the total can grow and everyone can win) and negative-sum (where the total shrinks and the group loses overall). Knowing which kind of game you are in is the whole point, because the winning strategy is completely different in each.
This distinction matters far more in money than most people realise. The stock market as a whole is positive-sum, because the companies in it produce real, growing earnings, but trying to beat other traders inside it is zero-sum before costs and negative-sum after fees, a point the economist William Sharpe proved in 1991. For the full argument, and why it means owning a broad tracker tends to beat trading after costs, read is the economy a zero sum game? and why passive investing wins. The same lens explains why you are not a horse in the AI economy and sits underneath why the UK won't tax wealth.
This guide is general education, not financial advice. Investing puts your capital at risk and the value of investments can fall as well as rise.
Frequently asked questions
What is a zero-sum game in simple terms?
It is any situation where the total never changes, so for one person to win, another has to lose the exact same amount. A game of poker between friends is the clearest example: the money on the table at the end is the same as the money that started there, just in different pockets.
What are examples of zero-sum games?
Poker, sports betting, most gambling, dividing a fixed inheritance, a penalty shootout, and two firms fighting over a fixed pool of customers are all zero-sum. In finance, the cleanest example is active trading against other traders, where you can only beat the average if someone else lags it.
What is a non-zero-sum game?
A non-zero-sum game is any situation where the total can change. It is positive-sum when everyone can gain at once (a trade both sides want, or long-run economic growth) and negative-sum when the group ends up worse off overall (a price war, or trading after fees are taken out).
Is a zero-sum game the same as a constant-sum game?
A zero-sum game is the special case of a constant-sum game where the constant is zero. In both, one player gaining means another loses, so strategically they behave the same way. The label "zero-sum" is just the most common shorthand for the whole idea.
Is the economy a zero-sum game?
No, not as a whole. Trade and production create new value, so the total pie grows over time, which is why real output per person has risen for generations. But specific arenas inside the economy, like housing and active trading, behave close to zero-sum. See the full argument in our article on whether the economy is a zero-sum game.
Sources
General information, not financial advice. Tax rules and figures can change; check the current position on gov.uk before acting.