The job of the agent is to bridge the seller and the buyer. The agent invested his time, effort and money to do this. It is humanely proper that you give commission. Normally, the seller is responsible to disburse that amount, about 3-5%, depending on the agent's request (subject to your approval) and/or based on your generosity.
Now, I just hoped that your buyer, upon proceeding to process the transfer, did not encounter problem with the documents you (as seller) and the buyer signed off. The completeness, compliance and authenticity of the deal is being secured by a broker. In every realty deal, a broker is required. This ensures buyers, that there has been a due diligence performed, papers are legal (it means that, provisions are securing both parties, especially the buyer, otherwise, this will be a future burden to the buyer) and the ownership of the property has been fully transferred and that the sale is absolute. A single document may not suffice.