This has actually been discussed in the Judge's discord. The IRL answer is that if it's G2, then the win for the match goes to whoever won G1. If it's G1 or G3, then whoever is up on prizes or whoever takes the next prize will win.
After a set amount of time (decided by an agreement between the players, if such an agreement can be reached, or 90 minutes if no such agreement can be reached), then we enter into an end-state:
If we have a player who won the only previous game, then they are the winner of the round. If players are tied on wins (at one each or zero each), then we go to whoever is up on prizes. And if there is a tie on prizes, then we go on whoever takes the next prize. Eventually someone is going to have to try to take a prize to win, and if they are successful, then they win.