What about having someone act as a bookie? Set an initial "odds" based on what you think will happen, then run the odds recursively so that as each bet is placed, the odds change to correct for the pool. Then the bookie just has to keep track of who has placed bets and what the odds were when they placed the bet. It could be done fairly easily in a spreadsheet, then you just need to worry about having a bookie for each fight who can keep the numbers straight (which shouldn't be hard).
Example. Moco bets 300K on Aikon at 3:5 odds against Flux. Then the odds shift a bit and Melyn puts 500K on at 33:50 (3.3 to 5) odds on Flux. The numbers used are arbitrary, but I think the idea is there.
You can tweak some values a bit if you want to improve the chances that the house ends up with some credits for their trouble, but it seems like a reasonable way to go about it. Actually, that may be how it's done in some systems, I'm more of a math man than a gambling one.
The beauty of this system is that the odds are basically crowd sourced. In the example, Ushanev and Melyn get 1:1 odds on their money because the betting was split exactly between duelist 1 and duelist 2, but if one duelist is heavily favored by the crowd, you can get substantially higher odds by betting on the underdog.
10 people bet 10 credits each on duelist 1.
2 people bet 10 credits each on duelist 2.
The total prize pool is 120 credits. If the heavily-favored duelist 1 wins, each of the people who bet on him will have a net gain of 2 credits (12 creds total minus the initial 10-credit bet). Essentially they are laying odds at 1:5, risking 10 credits to win 2.
If Duelist 2 wins, each person who bet on duelist 2 will have a net gain of 50 credits (60 total minus 10 initial bet). They are getting odds of 5:1, risking 10 credits to win 50.
Now the problem with this system is that your odds might shift significantly after you place your bet. Because of this drawback, I think there should be a point after which no more bets can be made followed by a summary of odds and a short period where bets can be withdrawn (not shifted to another duelist, just withdrawn for zero gain/loss). It IS possible to manipulate a system like this by placing and then withdrawing large bets, so everyone is on the honor system (or maybe there's a rule that bets over x amount cannot be withdrawn). It's either that or all bets are placed blind without knowing the odds and odds are only revealed after betting is fully closed (or even after the tournament is finished to prevent charges of throwing a match).
Vegas-style odds won't be possible, imo. Even if the bookmakers can keep track of them, getting that info out to all potential bettors in a timely manner would be a huge hassle -- not worth it for what is supposed to be a fun event anyway.