Exclusive Agency Listing
An "exclusive agency" listing allows an agent to list and market your home, guaranteeing them a commission if the house sells through any real estate agent or company. It also allows sellers to seek out buyers on their own.
This is not a popular type of listing agreement. The reason is that there is not much incentive for agents to spend money marketing your home. If you come up with your own buyer, they have spent money they cannot earn back through the real estate commission. Plus, it is too easy for a greedy buyer to go around the agent and negotiate directly with the seller.
If you find an agent willing to accept such a listing, do not expect too much from them. They will probably just place it in the Multiple Listing Service and sit around to see if something happens. A good agent would never accept such a listing, and you probably want a good agent.