For Double Elimination, use a standard double elimination tree. Players play until they have two losses. For Round Robin, use any round robin match setup where everyone plays everyone else. The winner is the player with the most victories, second is second most, and third is third most. For Ongoing Challenge, set a period of time that the tournament will take place.
Players can sign up at any time during the tournament.
Each entry gets you one character with 3 lives. If you lose three matches, you can join again. A player can challenge any other player wearing a tournament badge to play one game. A player only has to accept one challenge from any other player. A second challenge, using the same characters, may be refused with no victory or loss recorded.