你追我赶

nǐ zhuī wǒ gǎn

friendly one-upmanship

to try to emulate

你

nǐ

you (Note: In Taiwan, 妳 is used to address females, but in mainland China, it is not commonly used. Instead, 你 is used to address both males and females.)

追

zhuī

to chase

我

wǒ

I; me; my

赶

gǎn

to overtake; to catch up with