There’s a mechanic I’ve been thinking of lately, considering a game to put it in, where players determine an action order by showing fingers at the same time. So players count three, two, one-
And then everyone holds out a number of fingers equal to where they want to be in the turn order. So you could go first if you just hold out one finger. You could go second with two, and so on.
Except if two or more people show the same number, bam. They all get bumped back. If turns in this game are super fast, then that’s it: Everyone who picked the same number loses this turn and has to go for the next one. If turns are a little more elaborate, like a worker placement game, then the players who didn’t pick the same number as anyone else pick up, like, turn order tokens, then the players who remain have to go again. So if you pick 2, another player picks 4, and two players both pick 1, the player who picked 2 takes the 1st-place marker, the player who picked 4 takes the 2nd-place marker, and then the remaining two players have to fight over the 3 and 4.
So, players need to not get greedy, they need to pay attention to the turn orders their opponents are going for, and they need to know when they can get greedy. Maybe the game for this is super small, like a tile placement game where it’s just a matter of trying to place them well or cleanly?