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The phrase "zero sum game" is correct and usable in written English.
It is used to describe a situation in which one person's gain is equal to another person's loss. For example, "The negotiations between the two sides had become a zero sum game, with no room for compromise."
Exact(60)
And power IS a zero sum game.
For this is a zero sum game.
But this isn't a zero sum game.
Books are a zero sum game.
This isn't even a zero sum game anymore.
That's true if it's a zero sum game.
"It is not a zero sum game," said Kimmel.
"It is not a zero sum game," he said.
I've never seen it as a zero sum game.
They see the world through zero sum game lenses".
It becomes a zero sum game, you against him.
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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