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The different types of auction at Godaddy are given below
10 day public auction: These are the normal expiring domain auctions. The domains go through a 10 day bidding process. The highest bid at the end of it wins.
Closeout domain: If a public auction has not received any bids over the 10 days, it then goes through a 5 day reverse auction process. At this point this is a closeout domain and you can purchase it at any time at a fixed price. The domain starts at $11 for 24 hours. If no one has purchased it, it then falls to $10 for the next 24 hours and so on till it is $5.
Offer/Counter Offer: These are domains that have been listed by the sellers for auction. These are not expiring domains - therefore quite a few of these domains never end up being sold. The seller has an option to not sell unless he receives a bid he wants.
Offer/Counter Offer with a Buy Now: These are offer/counter offer domains where the seller has selected a price at which he has promised to sell the domain. These can be directly purchased by paying the Buy Now price or can be bid upon.