Customer: They are responsible for initiating the refund, and if required to respond to any questions about the refund/product in question.
Vendor: Generally they are responsible for product expertise, and approval of the refund to be processed.
Marketplace Owner: The MO is responsible for actually paying the customer back the funds (creating a credit memo). The reason for this is that the MO is the one responsible for the initial payment reception from the customer, therefore the customer needs to be paid back with the same payment method.
NOTE: Payouts and refunds are handled from the Marketplace Owner's account. Once an RMA for a refund has been processed, a credit memo needs to be created. If the MO has already paid out the order to the vendor, the MO will need to manually obtain the funds for the refund, from the vendor back to the MO account to pay the customer's Credit Memo out. Alternatively, the MO can absorb this payment first, and then get the money back from the vendor manually.