"Auction" versus "Bidding war" Real estate sales sometimes occur at an official auction.  But sometimes a seller who does not take their house to auction may find themselves entertaining multiple bids for the house.  In this case, the articles on real estate always seem to talk about managing a "bidding war".  What is the difference between a bidding war and an auction?  Are there regulatory issues that prevent a seller from converting their bidding war into a straight-up auction?  

(For instance, a seller with multiple bids could simply notify all bidders of the current highest bid, set a minimum bidding increment, and see if anyone bids higher, and repeat until one bidder is left.)
From a practical standpoint, bidding wars are effectively informal auctions. What is usually done is that the buyers inform their agents of their maximum price, and the buyers' agents tell the seller's agent "This is my client's bid, but please let us know if we're outbid." Sometimes this is formalized through what is known as an escalation clause, which is essentially an offer to bid some increment more than any other highest bid, up to some reservation price. 

Some sellers accept escalation clauses, some don't, and this decision appears to be influenced partially through strategy and partially through custom in the area. Not accepting an escalation clause can force buyers into what is effectively a first-price sealed-bid auction, while accepting them turns it into more of a traditional (English) auction.

As an additional note, the point that @desnep makes is true— while proof of other bids is required, it's not always possible to determine that those bids in fact represent genuine offers to buy. My understanding is that for this reason, when bids are expected to be few, buyers are encouraged to submit fixed bids and be prepared to walk away if they lose out, as there's a stronger incentive for sellers to fabricate bids (i.e., market manipulation is more effective in less-liquid markets).