The Grammarphobia Blog

Zero-sum games

Q: I see references to both “zero-sum games” and “zero-sum gains” on the Internet. Which is correct?

A: The term “zero sum” is widely misunderstood as meaning that nobody wins—or perhaps that nobody loses. In fact it means quite the opposite.

In any competitive situation, one side can’t win unless the other loses. “Zero-sum” means that when the losses are subtracted from the gains, the sum is zero.

The adjective “zero-sum” originated in the field of game theory in the mid-1940s, and it’s still commonly used to modify the word “game.” But “zero-sum” is also used to modify all kinds of nouns and to describe a wide variety of situations.

It would be inappropriate, however, to use it in the phrase “zero-sum gain.” That’s because “zero-sum” implies an equal balance between gain and loss.

We suspect that people are simply misunderstanding the phrase and hearing “gain” instead of “game.”

You’re right, though, that there’s a lot of zero-sum gaining on the Web. We got nearly 200,000 hits when we googled “zero-sum gain.” But we had nearly ten times as many hits for “zero-sum game.”

In game theory, as the Oxford English Dictionary explains, the adjective “zero-sum” is “applied to a game in which the sum of the winnings of all the players is always zero.”

In other words, the losses offset the gains, and the sum of losses and gains is zero.

But “zero-sum” is also used, the OED explains, to denote “any situation in which advantage to one participant necessarily leads to disadvantage to one or more of the others.”

So, for example, in “zero-sum diplomacy,” both sides can’t be winners.

The adjective was first used, according to OED citations, in John Von Neumann and Oskar Morgenstern’s book Theory of Games and Economic Behavior (1944):

“An important viewpoint in classifying games is this: Is the sum of all payments received by all players (at the end of the game) always zero; or is this not the case? … We shall call games of the first mentioned type zero-sum games.”

Here are a few more of the quotations cited in the OED:

“Perhaps the contestants in most important games nowadays (from labour disputes … to international diplomacy) too readily regard their games as zero-sum.” (From Stafford Beer’s book Decision and Control, 1966.)

“Everybody can win. Manufacturing is not a zero-sum game.” (A quote by L. B. Archer, from Gordon Wills and Ronald Yearsley’s Handbook of Management Technology, 1967.)

“C. Wright Mills … used a zero-sum conception of power (i.e., the more one person had the less was available to others).” (From the Times Literary Supplement, 1971.)

“We live in a zero-sum world.” (From the former BBC magazine The Listener, 1983.)

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