The house will be yours when the mortgage is paid. No provision in will. Retrospective analysis imposed on transaction. Would not be fair to couple to say that there was a bilateral contract since they would not want to be bound to pay the whole amount. But different contract formation process where sealed bids obtained.
Documents inviting sealed bids invariably modify the common law auction model.
Various types of sealed bids, but most significant context has been construction contracts. And as in other contexts, move away from rigid common law model of contract formation. Very common and important type of K formation situation Construction Contract tendering.