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A while back, someone decided to auction off something unique and valuable, as a silent auction: everyone would submit one bid only, and whoever bid the highest would win.

I submitted a bid that I thought would be higher than most people would pay, but I didn't win. He posted the final result, though, and the winning bid wasn't much higher than mine. If I had known it would go that high, I would have bid higher, and other people probably would have as well, which means he ended up leaving money on the table.

That makes me wonder: what is the point of running a silent auction if it can so easily be shown that it brings in less money than an auction in which people can openly bid against each other?

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But perhaps this is not always the case. The price might have been so high that you would not have been willing to bid above it. In fact it might have been so high that the no one but the highest bidder would have given that bid. Knowing this the highest bidder could decrease his bid. In fact in English auctions (non-silent rising bid auctions) the final price is the second highest valuation of the unique good. In the auction you describe (a sealed bid first price auction) the final price is usually somewhat random based on what people believe about each others valuations and each others bidding strategies. It can happen that the final price is higher than it would have been in an English auction because one of the bidders overvalued what his competition would be willing to pay. So the English auction is not clearly advantegous.

It has been shown that given some rather strict conditions the English auction and the sealed bid first price auction have the same expected yield for the auctioner. This is known as the "Revenue Equivalence Theorem".

In practice it is somewhat agreed upon that in rising price auctions bidders experience something called 'auction fever'. Basically being outbid encourages them to raise their own bid. This is true even if the auction was designed in such a way that revealing the true highest valuation by all bidders would be an equilibrium move. (Auction by proxy, the auction system eBay and several other sites use is such an auction type.)

So it seems that in practice you might be right and rising price auctions might be better in expected value for the seller. This is just speculation but in your case you I think you might merely be experiencing remorse because you have undervalued your competitor's bid. I have been there :)
(By the way this could encourage you to overbid on your next silent auction, to the benefit of the seller. Such overbidding might give him higher than English auction payoffs. Again, which system is better is not always clear.)

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