The buyer has just signed a buyer's agency agreement with a broker. The buyer has agreed to pay the broker a specific fee. Under the common law of agency, the relationship between the buyer and the broker would best be described as

"Agreement agency" is not a recognized term in agency law. While both parties may enter into an agreement, the specific legal terminology focuses on the nature of the agency itself, which in this case is express due to the explicit agreement on the fee and terms.

Implied agency arises when the actions or conduct of the parties suggest an agency relationship, even if no formal agreement exists. In this scenario, since the buyer has signed a specific agreement with the broker, the relationship is not implied but rather explicitly defined, eliminating the possibility of it being classified as implied agency.

Gratuitous agency refers to a situation where an agent acts on behalf of a principal without expecting any payment or compensation. Since the buyer has agreed to pay the broker a specific fee, this relationship cannot be classified as gratuitous, as compensation is a defining feature of the agreement.