I don't see the women being "captured", in the medieval sense. The guys in this particular setting would all see themselves as gentlemen and expert seducers. The "hunt" is a mental one...these are wealthy playboys who find marks and then do whatever it takes to lure them in, without resorting to kidnapping, or violence, etc. (A lot of the fun in this game could simply come from courtship)
Just to give an example...let's say Mike is a member of the society (I'll give it a name at some point, which will probably end up being the game's name), and he meets Laura, a successful investment banker...a really shrewd woman. Mike thinks Laura would turn a lot of heads at the next convention, and sets about seducing her. He calls her, invites her out, shows her a good time. They have great sex (Mike's obviously an expert lover). Little by little, he starts dominating her, and she finds herself submitting...there's that whole, "She's a bitch to everyone else...but, Mike just has 'something' that makes her swoon." Eventually, one day Mike makes her commit to trusting him fully, has her dress as sexy as possible, blindfolds her and takes her to the location of the Conclave. Once there, he tells her what's going on, etc. etc. etc. etc.
The women are "slaves" (or whatever they like to call themselves or have their 'owners' call them...there are no set rules for personal relationships), but more in the sexual sense. They continue their lives as normal, but their romantic and sexual lives belong to this society for however long she's of interest.
The relationships should be 1 on 1 for the most part. A dom with multiple subs would probably give one up to garner favor with another member....remember, these are all wealthy, influential men, and the society not only functions as a place to have all their kinky fantasies come to life, but also a place to network - acts done through the society could serve to grease up political gears or investments, etc. The casual "wanting" of each others' subs would lead to swapping, either for a night, or maybe permanently. For the slave to up and go with another dom, she'd have to be very very explicit, which she may or may not want to do...why slight a powerful man, after all? So there's room for intrigue among the submissives as well..."Why don't we encourage our masters to swap...you like mine and I like yours after all", etc.
If it'll make for a better game, then the society could enforce a strict 1-to-1 rule, and after considering the issue, it's likely that'll happen (plus, it'll make for smoother threads).
Another thing to consider is that a submissive could also simply fall out of favor with her master...with no one else to sponsor her, she's left in the outside without even a chance to look in. When she's being lavished with jewelry, or simply the affection and attention of such fine calibre gentlemen, she may not want to be left out.
And yet another point, I don't think this game is going to be violent. There could be some plotline that involves a rape, but that'll probably be the exception, and not the rule. Nobody wants an unhappy female at these functions, or some battered slave. Not only is that bad form, but these just aren't men who have to resort to violence to have their way.