The phrase "a competition with one" is correct and usable in written English.
It can be used to describe a contest or rivalry involving a single opponent or participant.
Example: "In this game, it's truly a competition with one, as I am only facing my toughest rival."
Alternatives: "a contest against one" or "a rivalry with one".
Then too, there's the flap about tension between older and younger workers, as if we are in mano a mano competition with one another for a foothold in the workplace.
If getting back in shape includes weight loss, then having a friendly competition with one another can be fun.
Politicians on the campaign trail performed as badly you can imagine -- at one point, it seemed as if candidates from both parties were having a local competition with one another to see who could back the most irresponsible travel ban policy the hardest.
Instead, nearly all of them have chosen to throw themselves back into a start-up, not so much because they want a spectacular new home or a personal jet — though many of them do — but because they are in a competition with themselves and one another.
The Romans, however, have been intermingled with the stock of the Ombrici and also, in some places, with that of the Tyrrheni 49 for both these tribes, before the general aggrandizement of the Romans, carried on a sort of competition with one another for the primacy, and since they had only the River Tiber between them could easily cross over against one another.
In 1983, Poon won a local art competition with one of his Wave paintings, helping to raise his profile and make him a sought-after artist for public commissions.
Instead, Homejoy cleaners are in competition with one another: On its internal system, cleaners can see how they rank by customer rating.
The various security services existed in a state of nervous competition with one another, and agents had to work harder and harder to show how diligent they were.
Over the weekend, over 200 teams of developers met up to participate in Node.js Knockout, a 48 hour coding competition with one basic rule: you *had* to use node.js to build your app.
Like most, I assumed they were cult-addled nuts, resistant to the progress of science and inexplicably in competition with one another for a spot on heaven's coveted 144,000-person roster.
There are only a few hundred houses on those blocks, and the wealthiest families find themselves in the real estate equivalent of a game of musical chairs, in competition with one another every time a parcel becomes available.
