There's so many different examples from Airbnb (12% host, 3% to renter), Uber (~15% to driver) to Craigslist (freemium w/ paid placement + posting) for pricing a marketplace. Is there a framework to follow when thinking through this model? Is there different pricing sensitivities per marketplace type (heavily curated vs. more open)?
Your business model is the difference between what the buyer is willing to pay, and what the seller is willing to accept. The key is pushing on both sides, getting customers to pay more (or pay more often), and getting sellers to accept higher fees, typically in exchange for moving more inventory.
Since you mentioned Airbnb, CL has apartment listing and it's quite popular, and there are no transaction fees. But it's a bit of a hassle to research a place, contact owner, schedule, make arrangements.
Airbnb makes is so convenient that people start renting apartments instead of hotel rooms. I didn't know they charge renters, but 3% is still much cheaper than hotel pricing.
At the other end, they deliver more booked days to property owners, you can take a surcharge if you help the property owner rent for more days out of the year.
So that's your typical business model: add convenience to one side, so you can move more inventory on the other side, for which you can charge a nice percentage.
As for open vs curated, consumers are risk averse, higher perceived quality results in more transactions and higher prices. Anything you can do to mitigate risk, whether its ratings/review, selective listing, insurance, etc.