Real estate brokers operate under the law of agency, which gives a broker the right to act for a principal in trying to buy or sell a property. In the basic principal-agent relationship of real estate brokerage, real estate brokers act in the capacity of a:

A special agent

Explanation:

An agent is a person who acts in the name of and on behalf of another, who has  been given  the degree of authority to do so.

A special agent is an agent that is authorized to  carry out  a specifically designated instance or in a specifically designated set of transactions or function. Any act out side the specific task or function authorized by the principal is not binding on the principal.  

For example the major duty of a real estate broker is to find a buyer for the principal’s property.  

Hence the best answer to the question is real estate brokers act in the capacity of a Special agent