What specific structural things are important?
Airbnb did this beautifully: they set up insurance for all their hosts, and so were able to frame "stay on our platform" as a safety directive.
You can also go the opposite way, but that usually leads to user-hostile antipatterns. E.g., Freelancer tries to detect all the ways folks might send each other phone numbers on their messaging service. This is both annoying and easy to circumvent.
If your rate of defection is high enough, no amount of tactical tricks will save you. Incentive and ingenuity together are too much.
When you're small and still have structural degrees of freedom, target the incentive by adding value to your offering if you can. If the problem only appears when you're big, you may have the resources to play whack-a-mole.
If you're small, have high defection rates, and also can't economically add value to your offering - it's time to move into another line of business.
I sell a lot of expensive stuff on the web, and I'd say 80% of my buyers are repeat buyers that started contacting me through mail after a couple of deals.
It works since Airbnb is mostly there to hook you up and protect from crazy people's wanton destruction, so once you know you're dealing with safe people and you've gotten the review, eh.
Wouldn't really be worth the penny-pinching, except people tend to forget about the long-term booking discounts and actually end up paying more than they would've just using airbnb.
That's the value they provide and the stick. It works because trusting third world developers is hard. It fails for more local developers.
Speaking from extensive marketplace experience: A pattern of long term relationships will lead almost surely* to supply-side defection in your marketplace, which is when the supply leverages its relationship with the demand to set up a side deal that cuts out the platform. This can quickly take both supply-side and demand-side churn to levels that are an existential threat to the business. And of course, fraudulently inclined supply side firms may turn defection itself into an optimized business process if it's lucrative enough to do so.
High defection rates ultimately killed Poppy (babysitting marketplace) and Tutorspree (tutoring marketplace), and they continue to plague even platforms like Rover and Airbnb despite (or because of?) their scale.
* Despite what many folks believe, it's is possible to run a successful relationship marketplace without significant supply-side defection; you just need to structure it to leverage the relationship, rather than trying to break the relationship into a set of one-off transactions. (As an existence proof, I'm running such a marketplace right now.)