To what extent is a mediator entitled to a commission if he completes a new deal with a buyer to whom he was introduced by another mediator in a previous, uncompleted deal?

The broker is not obligated to give anything to the property owner if he concluded an independent deal with the buyer after the first transaction, because he is not entitled to anything except in the first transaction where he exerted effort. As for subsequent sales, he is not entitled to anything in them due to the absence of any work on his part. Therefore, the questioner is not obligated to give the first broker anything; if he does, it is considered a donation.