What is the ruling on money acquired by a person from a public auction, where another participant pays him a certain amount for not participating in the auction, and this is done with the consent of both parties? And why?

It is permissible for some, but not all, bidders in an auction to forgo further bidding in exchange for compensation paid to them, because requesting this from all of them would cause clear harm to the seller. Jurists have explicitly stated the permissibility of this, even if it involves compensation, as in their saying: "Refrain from bidding further and you shall have a dirham." The compensation becomes binding whether the one who requested it buys or not. Some have stated that this does not fall under consuming people's wealth unjustly, but rather it is a relinquishing of a right for compensation.