Wa`alaykum as-salamu warahmatullahi wabarakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us. We implore Allah Almighty to help us serve His cause and render our work sincere for His Sake.
According to the Islamic Shari`ah, the basic principle with regard to transactions is permissibility unless there is a specific injunction indicating otherwise. Only when the general Islamic parameters that secure justice and fairness are infringed upon, a particular transaction turns to be impermissible.
Shedding more light on the issue, the prominent Saudi scholar and lecturer Sheikh M. Saleh Al-Munajid, states,
Islam permits selling by auction and does not forbid it, according to the most correct and well-known opinion of the scholars. This is based on the following proofs:
1 – Jabir said: A man had decided that a slave of his would be manumitted after his death, but later on he was in need of money, so the Prophet (peace and blessings be upon him) took the slave and said, “Who will buy this slave from me?” Nu’aym ibn‘Abd Allah bought him, and he (the Prophet (peace and blessings be upon him) handed the slave over to him. (Al-Bukhari and Muslim). Al-Bukhari included this hadith in a chapter titled “Bay’ al-Muzaayadah (Selling by Auction).”
Ibn Hajar quoted Ibn Battal as he said: The words of the Prophet (peace and blessings be upon him) in this Hadith, “Who will buy this slave from me?” indicate that he was offering him to the highest bidder so that the needs of the bankrupt man for whom he was selling him could be met. (Fath al-Baari, 4/354)
2-`Ataa’ said: I met some people who saw nothing wrong with selling booty to the highest bidder. (Al-Bukhari)
Rational evidence: In an auction, the vendor offers his goods for sale, and the purchaser offers to buy them for a certain price. If the vendor does not accept that price, that is the end of the matter and there is no transaction. Then he will say, “Who will offer more?” A second purchaser can then offer a higher price, and so on. In this case, each offer is a separate and independent deal; and there is nothing wrong with that.
Allah Almighty knows best.
Excerpted, with slight modifications, from www.islamqa.info