Question
It seems that support for a marketplace could be consider a competitive advantage if it's tightly integrated into the transaction, so should this be built in house, or use a 3rd party app to do this.
What do AirBNB, Fivver, Thumbtack use?
Answer
Your support software should cater to your needs, depending on how your business operates.
Fiver uses Vanilla forum and Zendesk.
Thumbtack uses Zendesk.
Not sure about AirBNB, their help center seems to be custom.
Depending on how well funded your are, I would recommend starting with a free plan with one of the help desk SaaS products, or even using open source ticketing platform. Then, as your needs grow and you need integration with your marketplace, there's no reason you can't scale and migrate.