Unfortunately, two of the four players... aren't fans of direct conflict or player elimination.
I love King of Tokyo, too. I like direct conflict and am fine with player elimination. I also love Euros that have neither. I'm a gamer through-and-through, I guess.
Most aren't this easy. :)
So, ahem, re-read your line above again. It seems to convey all you needed to know ahead of time. So maybe next time, no King!
--David