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"a zero-sum game" is a correct and commonly used phrase in written English.
It is typically used to describe a situation or activity in which one person's or group's gain is exactly balanced by another person's or group's loss. This phrase is often used in discussions about competition, economics, and business strategies. Example: Negotiations between the two companies turned into a zero-sum game, with each party trying to gain the upper hand and refusing to make any concessions.
Exact(57)
"It isn't a zero-sum game".
But irredentism is a zero-sum game.
"We're nearing a zero-sum game.
College admissions are a zero-sum game.
Politics became a zero-sum game.
It is not a zero-sum game.
Governing is never a zero-sum game.
Education is not a zero-sum game.
Longevity is not a zero-sum game.
Public spending is a zero-sum game.
This is not a zero-sum game.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com