pun-upmanship

A situation in which two or more people trade an ever-escalating quantity of puns on a given topic, ending only when all except one have quit due to tiredness/boredom/psychosis/etc.

(Upon seeing that it's snowing outside)

Person A: "Snow it begins!"

Person B: "Snow comment."

Person A: "Why do you have to be snow cynical? If you don't like it, you could at least flake it."

Person B: "Whoa! Don't get flurrious with me just because you can't sleet things from my point of view."

Person A: "I have to admit: I wasn't expecting such a chilly reception. Anyway, you may be a bit of an ice queen right now, but I bet you'll warm up to things eventually."

Person B: "... You win."

Person A: "Ha! In pun-upmanship, there can only be pun!"