Sarna's info is supposedly taken from
MechWarrior's Guide to Solaris VII but, contrary to Sarna says, the book has bush league fights (where twenty to thirty MechWarriors all fight each other over the course of a year) being more common than single- or triple-elimination tournaments; and I haven't found anything yet in the book to back up Sarna's claim that the grand tournament has 128 competitors.
The first two RPGs (set in 3025 and 3050 respectively) say a contestant needs to win seven to nine total matches for a championship. That's for games held every three months, and it doesn't specify how the tournaments are structured.
When Justin Xiang arrives on Solaris VII in
Warrior: En Garde, he basically tricks his way into good initial standings, and again it isn't clear how the grand championship is structured. We do at least learn that the Solaris Champion fights in the "Open Class" and doesn't have to accept challenges from MechWarriors whose 'Mechs are too light - a
Centurion is too light for the Open Class, whereas a
Rifleman is not. (I assume a
Griffin is also too light but we don't know for sure.) We see a "Medium Class" fight between a
Hermes II and a
Vindicator, and an "Open Class" one where a
Rifleman fights a pair of
Vindicators.
The Solaris VII Boxed Set says there's a feeder system of smaller arenas which usually handle the lighter weight fights. Most successful fighters spend some years in the feeder system (I suspect mainly to develop contacts and learn how to work publicity). The boxed set is based on an article from the BattleTechnology magazine which adds more detail- small towns sponsor exoskeleton fights, and get a share of network profits as their local champion works their way up to the big city circuit; the big city circuit is divided into 8 levels, where a fighter can only challenge others on the same level or one level higher; and any fighter with 12 or more kills can decline a challenge from anyone without at least 12 kills.
I think expansions talk more about the bush leagues, and add competitions (like races, king of the hill, and so on) that aren't simple fights to the death.
The new Stackpole stories (
described here) seem to describe a more traditional bracketed structure.
Granted, each of these snapshots are set decades apart - the tournament system may be changing over time.