MGPM used the normal daytime tiebreaker in the first season when it was a two round game. The SUdden Death tiebreaker was always used in the three round game format of MGPM, unless the players were tied 6-6 before the third round began, which I think did happen once.
On the Daily Syndie run of MG, the sudden death tiebreakers would often be played on Thursday or Friday episodes as the contestant's two games would not straddle from Friday into MOnday.
In most if not all cases, Sudden Death tiebreak questions in which none of the celebs matched a contestant were edited out(when Dawson was still on the show, Gene only got answers from Brett, CHarles, and Richard, after Richard left, he would get responses from all six celebs). One time Gene mentioned on air that they were on their third go-round with a Sudden Death question, but the first two failed attemps were edited out.
If both contestants wrote down the same answer, a new question would be asked and the players would write down their answer, and the original question would be edited out of the program.