What is the general name for this particular game mechanic?

Question

I'm hoping to find a common general terminology for a mechanic I have encountered in several board games.

As an example, here's an excerpt from the rules for The King's Dilemma:

At the end of your voting turn, if you are now the player with the most Power [tokens] on your Vote (no matter which side you chose), you immediately take the Leader token. Do not take the Leader token if you only equal the highest bidder’s amount of Power [tokens].

The general idea is that, if you have (say) 3 tokens on the space I want to control, it's not enough for me to put 3 of my own tokens on it; I have to put 4 or more to be in control. And if I do put 4 tokens on it (thereby gaining control), it's not enough for you to then add a 4th token of your own—you'd need to bring your total number of tokens up to 5 or more to regain control.

Is there a general term for this mechanic?

Answer 1

This is called first in wins.

See for example this article on game design

First in wins. Markers placed later are considered to fall behind those placed earlier. The only way a later player can get ahead is to exceed the previous count. This is generally best if the game has a start player disadvantage.

This is in a broader class of tie-breakers favoring efficiency, which one author categorizes as epsilon tie-breakers:

The efficiency argument and even the game balance factor are a restatement of the epsilon argument addressed above. The game balance point is perhaps a little more subtle, but in essence is the same as the many majority/plurality games which state that the first one in is the default winner of the contest (eg Medieval Merchant, Die Neuen Entdecker, etc): another phrasing of epsilon.

(which I found interesting because of the default formulation of this rule: "first one in", a form of "first in wins")