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The phrase "cooperation without" is grammatically correct and can be used in written English.
It is typically used to describe a situation where cooperation is lacking or absent. Example: "The project was hindered by cooperation without clear communication between team members."
Exact(54)
The evolution of sociality and altruism is enigmatic because cooperators are constantly threatened by cheaters who benefit from cooperation without incurring its full cost [1, 2].
The central problem is that cooperation is often metabolically costly to individuals thus, all else being equal, cheats that reap the rewards of cooperation without making any investment should be able to invade populations of cooperators [5].
The central problem is that investment in the public-good is costly to individuals yet the public-good may be used by others, thus, all else being equal, cheats that reap the rewards of cooperation without making any investment should be able to invade a population of cooperators [ 2].
In 2005 she co-authored Cooperation without Trust?
Panchanathan, K. & Boyd, R. Indirect reciprocity can stabilize cooperation without the second-order free rider problem.
There is no ignoring the role of Baghdad's game of cooperation without content in this diplomatic debacle.
Similar(6)
Instead of paying attention to those issues, we simper about mutual respect and cooperation--without acknowledging the fact that China is today the world's most powerful Evil Empire.
With this method, people can attend to the cooperation system without any changes.
Nothing is gained, except that in such cases Honest is paying the cooperation cost without getting the benefit.
The scheme without cooperation is the protocol without the secondary system and the Relay.
Proceeding without cooperation from pilots could invite their opposition.
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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