Overtime

I've been working on implementing a simple overtime feature that will extend the game if it ends in a tie.
For "rapid scoring" games, such as Bitmatch, Rabbit, and HTF, the game time is extended in increments of 20 seconds until there is a winner.
For "event scoring" games such as CTF and ZC, the game goes into an indefinite period of sudden death, where the game ends when someone scores.
For Nexus, the Nexus is opened (and will remain open for the rest of the game), and time is extended in 20 second increments as in Bitmatch games.
For Core, I'm thinking the game will enter a sudden death period, and cores will slowly degrade. First team to get ahead wins immediately.
This all kind of makes sense, but I am running into issues that do not currently exist in the game.
1) What if there is only 1 player, or players on only 1 team. Should the game be extended? If not, who wins?
1a) If there are two teams when the normal game ends, each with 0 points, and only the first team has a player, what happens?
2) What if all the players quit such that situation 1 happens in the middle of sudden death? Should the game just be ended? Who would win?
3) What if there are three teams, A, B, and C; A & B are tied for first, C is losing, but only A and C have players? What should happen then?
... and so on...
For "rapid scoring" games, such as Bitmatch, Rabbit, and HTF, the game time is extended in increments of 20 seconds until there is a winner.
For "event scoring" games such as CTF and ZC, the game goes into an indefinite period of sudden death, where the game ends when someone scores.
For Nexus, the Nexus is opened (and will remain open for the rest of the game), and time is extended in 20 second increments as in Bitmatch games.
For Core, I'm thinking the game will enter a sudden death period, and cores will slowly degrade. First team to get ahead wins immediately.
This all kind of makes sense, but I am running into issues that do not currently exist in the game.
1) What if there is only 1 player, or players on only 1 team. Should the game be extended? If not, who wins?
1a) If there are two teams when the normal game ends, each with 0 points, and only the first team has a player, what happens?
2) What if all the players quit such that situation 1 happens in the middle of sudden death? Should the game just be ended? Who would win?
3) What if there are three teams, A, B, and C; A & B are tied for first, C is losing, but only A and C have players? What should happen then?
... and so on...