Is there a name for this game design?

Where those that are losing are given an advantage or those in the lead are given disadvantages in the name of competition?

For example: in Mario Cart if you are in the lead the cars behind you go faster than normal.
In The Amazing Race, there are stops and rules put in place that make the leaders wait so those behind can catch up

In racing games, it’s often called rubberbanding.

That’s the term that immediately came to mind, and I use it more expansively, outside the raving genre. Don’t know if it’s just me or if I picked up the expanded usage from someone. I think I first heard the term with RC ProAm.

Seems like that would work for penalizing leaders, The rubberband is pulling them back to the competition.

I don’t know if the direction matters, but the way I’ve always used it is that the laggers get rubber banded forward to catch up to the leader. Casual research indicates that this is the general direction it is used in and that it is not exclusive to racing games.

Handicapping.

Handicapping is typically something done before the handicapped event starts, though, not something applied during the event itself.

And after each contest, the handicap is generally adjusted up or down based on performance so that each contest between the same contestants will always feel competitive.

Generally in board games it’s called a “catch-up mechanic”.

I would have used the word “handicapping”, also. “Rubber-banding”, in a video game context, more typically refers to one common result of lag, in an online game: You move somewhere, but your client is out of communication for the server for a moment, and when the connection catches up, the server puts you back where it thinks you should be, and you get pulled back to where you moved from.

This is what they call it in videogames also I believe.

The generic game design term would be a Catch up feature. It’s something the game does to help those who are losing get back in the game.