This is the 1896th most frequent Japanese word.
競う
To compete.
In this sentence, '競う' is used to describe direct competition between individuals who are striving to achieve the same goal.
二人はスポーツ大会で優勝を競っています。
The two are competing for the championship in the sports tournament.
Here, '競う' refers to a contest of ideas where individuals compare their concepts or opinions in a positive or constructive manner.
彼らは友好的にアイデアの良さを競った。
They amicably competed over the quality of their ideas.
In this usage, '競う' indicates rivalry between entities, such as cities, in a particular field or domain to enhance or achieve something.