outdoes, outdoing, outdid, outdone
1) VERB If you outdo someone, you are a lot more successful than they are at a particular activity.

[V n] It was important for me to outdo them, to feel better than they were...

[V n] Both sides have tried to outdo each other to show how tough they can be.

2) PHRASE: PHR with cl You use not to be outdone to introduce an action which someone takes in response to a previous action.

Not to be outdone, the Croats came up with a peacekeeping proposal of their own...

She wore a lovely tiara but the groom, not to be outdone, had on a very smart embroidered waistcoat.

English dictionary. 2008.