Are eBay auctions efficient? A model with buyer entries

I use a sequential-auction model to mimic the environment of Internet auction sites, such as eBay. For a sequence of auctions, new buyers may enter the auction site after some of the auctions has completed and only bid for the remaining auctions. Because an incumbent buyer may have revealed their own valuation in earlier auctions while a new entrant do not, their expectations about the future are asymmetric. As a result, a buyer with a lower valuation may win an auction while a buyer with a higher valuation may restrain from bidding higher, resulting an inefficient allocation. On the contrary, selling the multiple items in a single simultaneous auction results in an efficient outcome. The profit from selling all items together in one simultaneous auction is less than that from selling them sequentially.