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The phrase "agree on exchanging" is correct and usable in written English.
It can be used when discussing a mutual decision to exchange something, such as information, items, or services.
Example: "After much discussion, we finally agree on exchanging our resources to benefit both parties."
Alternatives: "consent to exchange" or "reach an agreement to exchange".
Exact(1)
Our idea is to start from a railway timetable proposed by an Infrastructure Manager (IM), whose efficiency may be improved, involving a small number of agents, operating trains on the same line in a short period of time, that agree on exchanging more information on their preferences, moving from a non cooperative setting to a cooperative one.
Similar(59)
To explore the added value of close cooperation and to reconsider the design, execution and interpretation of animal feeding trials as well as in vitro and in silico approaches, the above-mentioned projects agreed on exchanging material and data and are performing subchronic, chronic and carcinogenicity studies with two GM events in a highly coordinated manner.
If the teams were unable to agree on the exchange, Rozelle would decide through arbitration what the compensation should be.
We could do it directly, but then we have to agree on an exchange rate and there's no paper trail.
Distributed mechanisms for allocating indivisible goods are mechanisms lacking central control, in which agents can locally agree on deals to exchange some of the goods in their possession.
The EC said it has evidence that competitors agreed on prices, exchanged commercially sensitive information and allocated customers to the cartel in the mid-1990s.
Lobo and Lele agree to exchange Charlie for Guddu and Sweety on a train.
In the case that it won't be able to agree on a state exchange, Minnesota would default to a federal exchange.
Barring a surprise ruling by Germany's constitutional court (which is hearing a case objecting to the start of monetary union), Germany, France, Italy, Spain, the Netherlands, Belgium, Austria, Finland, Portugal, Ireland and Luxembourg will agree on locking their exchange rates on May 1st.
In this way, a market can also be conceptualized as a self-adjusting monetary incentive system that influences the behaviour of consumers and providers so they agree on terms of exchange.
Both he and Mr. de Villepin said they had agreed to exchange information on radical clerics and on the protection of high-profile terrorist targets.
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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