Tiebreakers are typically used when multiple combatants can take an action from the same trigger. (e.g. A character adjacent to two enemies moves away without shifting, provoking an OA from both enemies.)
I recently ran a one-shot of the Zombiegeddon premise, as first laid out in the epic Lessons from DMing with my GF thread. Since I only had three players, I needed to bulk up the party, and opted to use companion characters (as detailed in the DMG2).
The background premise I came up with was that a radical splinter of the recently-disbanded Dustmen found a new portal from Sigil to the Prime plane, in the coastal city of Edge. Only problem was any of their undead troops they tried to bring through ended up being resurrected to life.