We did have a third-place tiebreaker (only prizes for top three teams) at my NN14 pub quiz which the participants were happy to do as trial-by-combat, but we had them go back-and-forth naming MI's congressional delegation instead. Photo here: https://www.facebook.com/NetrootsNation/photos/a.10152533453109827.1073741835.54730664826/10152541814214827/?type=1&theater
FWIW, the pub quiz I've been frequenting of late has two different types of tiebreakers--for first place, a 5 question round, with team getting most correct answers taking it all. For Second/Third place, a question with a numerical answer (a la Wits and Wagers) with closest team taking it--e.g., "Combined, how many Baby-Sitters Club and Sweet Valley High books were there (main series only)?," "By surface areas, how many Great Salt Lakes could fit into Hudson Bay?"
I had never seen that before! And it happened so quickly - before I even understood how it would work, the game was over. Strange. Wonder why they can't just declare a tie?
I'm assuming it's in the rules. Normally, if at the end of a game, there's a tie, both are returning champions in the next game. This was at the end of a tournament final, so no returning champions, and involved combining totals for two days, which makes a tie SUPER unlikely.