Longman Dictionary of Contemporary English homepage

outdo

verb
     
out‧do past tense outdid past participle outdone third person singular outdoes [transitive]
1 to be better or more successful than someone else at doing something:
When it comes to speed of response, a small firm can outdo a big company.
outdo somebody in something
skaters trying to outdo each other in grace and speed
2

not to be outdone

in order not to let someone else do better or seem better than you:
Not to be outdone, other computer manufacturers are also donating machines to schools.

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