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The phrase "higher level of cooperation" is correct and usable in written English.
You can use it when referring to an increased degree of collaboration between two or more groups or individuals. For example, "The executive team decided to seek a higher level of cooperation with our competitors in order to increase profits."
Exact(10)
The S.E.C. may well be using the nonprosecution agreement with Ralph Lauren to reinforce its position that it wants — and perhaps even expects — a higher level of cooperation from companies that discover violations.
Country dyads governed by treaties with a larger sum of institutional mechanisms likewise evince a higher level of cooperation, although certain institutional mechanisms appear to be more important than others.
Mr. Gilman said today that Congress was demanding tighter surveillance of North Korea and a higher level of cooperation from Pyongyang, where Kim Jong Il, the son of the late dictator, Kim Il Sung, is expected to be inaugurated as President next week.
Information sent by insiders was often better received and could result in a higher level of cooperation.
Interestingly, for the three schemes, higher level of cooperation can increase both NEE and NC because of better exploiting inter-cell interference.
Considering the age group, it was observed that adult patients presented higher level of cooperation (median 82.2) than adolescents (median 64.5).
Similar(50)
Species with higher levels of cooperation in parental care have been hypothesized to be more strongly territorial.
Prior results from experimental economics show that acts of free riding are sometimes punished, that punishment deters free riding, and that the risk or actuality of punishment recruits higher levels of cooperation in a joint effort.
Put differently, when some individuals initiate cooperation, others learn to trust them and are more willing to adopt reciprocity themselves, leading to higher levels of cooperation.
The new balance between where within-group competition is reduced, along with increased group competition, should promote higher levels of cooperation in individuals (Bowles [2006]).
The communication may contribute to higher levels of cooperation because it enables social learning (Deadman et al. 2000; Poteete et al. 2010).
More suggestions(15)
higher level of interactions
higher level of contacts
increasing level of cooperation
higher level of integrated
elevated level of cooperation
higher level of associated
higher level of complexity
higher level of tutor
higher level of sophistication
higher level of discourse
higher level of purity
higher risk of cooperation
higher level of land
higher degree of cooperation
higher level of detail
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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