The house is to be sold in/for auction.
Which preposition is appropriate?
Is it in or for?
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The more common preposition to use would be "at," and "by," and "in."
If you are using the word "auction" as a verb:
The house is to be sold by auction.
The house is to be sold at (an) auction.
The house was sold in the auction.
This is a list of the most expensive cars sold in auto auctions.1
For would be wrong in your context.
The house is to be sold for auction.
can mean that the house is being sold to fund an auction.