It is an interesting display. The males come out to the lek to impress a female and to discourage other males. The males may strut around an area that they deem to be theirs and aggressively confront any other male who might attempt to walk through or claim the same piece of turf. When females are present the males will put their head down, tail straight up in the air shoulders forward and wings out to the side inflating purple neck sacks and do a rapid tippy-tap dance around and around to try to impress a mostly disinterested female. Sometimes the males are beak to beak doing their dance, trying to out-do the other male. Sometimes they get very aggressive, jumping up in the air and coming down feet first on top of the other male. When the females wander off in to the taller grass most activity stops until a female returns. This goes on for an hour or two after sunrise and then the birds leave, to return again tomorrow to start over again. I don't know at what point a female selects a male to breed with, but I understand that she is on her own to lay er eggs and tend to her nest and young after breeding.
Lots of photos below. Click an image to see larger. Captions below the photos.