Round robin tournament
The Round-robin is a style of tournament where everyone fights everyone else. This appears superficially fair since everybody gets a chance, even the less experienced.
This major disadvantage is the increasing number of bouts as number of contestants rises (3 for 3 fighters, 6 for 4, 10 for 5, 15 for 6, but then 21 for 7, 28 for 8 and 36 for 9) which can make for long sessions (with the audience perhaps getting bored, if not the combatants -- how many times can you watch Squire Should-Have-Lost-Weight having his helm smashed in ?). Some fighters may also get tired waiting their turn, especially as time creeps on.
There is also the issue that, in later rounds, cunning tactics come into play, as individual opponents' weaknesses are analysed, and styles and weapons used are varied to take advantage of these.