How can the observed strategies* in this actual auction be explained?

Question

This is a "real world" question.

Recently I witnessed the separate auctions of about 30 houses. The place where I went uses the following rules. The following describes the procedure for the auctioning of a single house.

First, an English auction is held (as far as I could tell, without a hidden reserve). The highest bidder "A" at the end of this round is invited to come forward and show identification and proof of his/her ability to pay the bid plus costs and taxes.

Then a Dutch auction is held (of the same house), starting much higher. All can participate. If any bidder "B" (or "A") accepts a price above the winning bid of the first round, then he wins the overall auction and is invited to come forward and show identification and proof of his/her ability to pay the bid plus costs and taxes. If the price reaches the bid of the first round, then bidder "A" wins the overall auction.

Now, it might occur to you that there is something very wrong with checking the validity of "A" and "B" only. At least, that occurred to me. But that is not the question.

The question concerns the strategies* that I think I observed. In almost all cases there was vehement bidding during the first round (up to an average of EUR 100,000). In the end stages three or two bidders would remain active. But during the second round I never saw an accepted price more than EUR 2,000 higher than the highest bid of the first round.

(I also noticed that most active participants appeared to be professionals or, at least, regulars.)

The only explanation that I could come up with was that perhaps none of the bidders really know what each house is "worth" (whatever that means), and therefore they heuristically and risk-aversely rely on the other bids, making sure that they are never more than a couple of EUR 1,000 higher. And that, since they learn nothing during the second round, they use the same threshold there.

But I figure that can hardly be an equilibrium. Why would you drive up the price in the first round if you could "always" pick it up in the second round for EUR 2,000 above a (much) lower price?

Or is this perhaps evidence of collusion and/or convention and/or stupidity?

Can anyone please explain the strategies* that I observed?

*Technically: actions

This video shows how the auction works.

It's in Dutch, but you'll see the following things happen.

4:16 The auctioneer asks for a first bid.

4:20 EUR 20,000 is bid.

5:56 The highest bid is recorded at EUR 42,000.

6:16 Round 2 starts at EUR 42,000 + EUR 60,000 = EUR 102,000. (This auctioneer makes it easy for himself by just mentioning the difference between round 1 and round 2 prices, instead of mentioning the full price, as I saw another one do.)

7:04 The winning bid is recorded at EUR 42,000 + EUR 5,000 = EUR 47,000.

Of course, this is a counterexample to my 30 observations, but I take it that otherwise it wouldn't have made such an exciting instructional video.

Edit. I recorded some of the bids and prices. As you can see, I forgot about three cases between EUR 2,000 and EUR 3,000. So, where I said "EUR 2,000", I should have said "EUR 3,000". Sorry about that.

initial bid round 1
 |  highest bid round 1
 |   |  initial price round 2
 |   |   |  final price round 2
 |   |   |   |
  5  16  80  16.7
 50 140 250 140.9
 50 125 350 125
 30  59 150  59
 40 112 300 114
 40 117 300 177.3 (possibly a typo)
 50 130 400 132
 30  79 250  81.5 (oops)
 30  68 250  68.4
 40  62 200  65   (oops)
 20  66 250  69   (oops)
100 274           (invalid)
234 234 500 234   (restarted)
 50 171 300 171
  5  45 150  46
 10  74 250  74.2
 40  71 250  72.2
 40  67 250  68.8
 40  87 300  87.6
 40  82 250  82.1
100 225 450 225

Answer 1

Given that most of the bidders are regulars, it smells a bit like an iterated-prisoners-dilemma situation. As long as the bidders all honor a tacit agreement to bid up to, say, 2000 below their subjective limit in the first round, this limits how much of the span between the subjective limits of the highest and next-highest bidders will be scored by the seller.

Viewed in isolation, a single bidder who thinks he might have the second highest valuation of a house would benefit from staying passive during the first round and then bidding in the second round at 2500 above the first-round price. However, doing so would make the other professionals defect in subsequent rounds too, and everybody would end up paying more. In the end that could cost the initial defector more than he gains from the initial breach.

Answer 2

I think this behavior is also consistent with the idea that all the bidders are (nearly) perfectly competitive/rational specimens of homo economicus. If I come into the auction with a fixed belief about the price of the house, I'm better off bidding up to that price in the first round — with the hope that everyone else stops bidding at some point below my price and I can get the house for cheaper — than in the second round, where I have to immediately bid my price or risk being undercut. That is, an English auction is game-theoretically similar to a Vickrey auction (the differences being that price discovery is possible, and that the bid increment is finite). On the other hand, a Dutch auction is game-theoretically similar to a first-price sealed bid auction, which is less favorable to the bidders.

To put it another way, if I'm willing to bid in the Dutch half of the auction, why wouldn't I have been willing to make the same bid in the English half?

Answer 3

It sounds like the participants have a solid decision on what they are willing to pay for a given house and expect that the other valuations will be close to theirs. In that case, there is no benefit in winning the first auction cheaply as you will simply be outbid in the second. Think if the house is worth 100,000 and you win the first at 50,000. Also, if I win the first auction but am willing to bid in the second I should have saved my breath the first time.

It seems my objective should be to win the first auction at a price high enough to stand up in the second and a little below the maximum I am willing to pay. Maybe there are bid increments to help. Say I think the house is worth 100,000. It seems I should bid 98,000 in the first. Then maybe if the increment is 2,500 my bid will stand up.

Answer 4

Let $v_i$ be the valuation of the bidders. Then English auction extracts the second maximum, and Dutch auction extracts $\frac{n-1}{n}v_{max}$. The idea to combine those auctions is to get $\max(v_{\text{2nd } max}, \frac{n-1}{n}v_{max})$.

However, the first auction gives some estimates, how high the bids are (and those are usually close). So keeping my bet high I broadcast some information about my valuation, and thus making other betting higher in the second stage (i.e. if I can't get the house cheaply, let them pay for it).

Of course, this is just a guess ;-)

Answer 5

If you have the same participants bidding on the same house, then regardless of whether it's an English or Dutch auction, you would generally expect the house to sell for the same price on average. So in a sense the second auction is redundant. You might see the same effect if they simply ran a second English auction after the first, and went with the higher bid of the two.

Specifically, assume that each bidder has a set threshold price. They will continue bidding up to their threshold price in an English auction, and they will stop the clock when the price drops below their threshold in a Dutch auction. Either way, the person willing to pay the most for the house should win.

You might argue that in the English auction, the expected outcome is that the winner will get the house for the second place bidder's threshold plus epsilon, while in the Dutch auction the winner should pay his full threshold price. But since the Dutch auction is after the English one, the winner has a pretty good estimate of what the second place bidder's threshold is, and can safely adjust his threshold down to the second place threshold plus a safety margin to account for uncertainty. Thus the Dutch auction price will be the English auction price plus whatever safety margin the winner chooses to add, which seems to be between EUR 0 and 2000 in practice. Of course, anyone who changes their threshold between the English and Dutch auctions is free to outbid the previous winner, thus driving up the Dutch auction price further away from the English auction price. But apparently this doesn't happen past about EUR 2000.

Edit: In my answer I'm ignoring any strategy that takes advantage of the fact that there are two auctions in a row. Such a strategy would involve not bidding according to one's actual threshold, but instead bidding in such a way as to deceive others about one's threshold. I suppose any major divergence between the first and second auction prices would constitute evidence of such shenanigans.

Edit 2: Upon further consideration, there are really only two "shenanigan" strategies I can think of: bidding above one's threshold and bidding below it. Bidding above is of course extremely risky, and the only potential benefit would be to push someone else to bid more for an auction that they're going to win anyway.

Bidding below one's own threshold (i.e. stopping before the bidding reaches your threshold) has more potential: if you have the second-highest threshold among bidders, stopping early in the English auction can deceive the top-threshold person (your only competition) into thinking your threshold is lower than it is, with the result that the English auction price will be below your threshold. Then, in the Dutch auction, if your opponent gets greedy, they might try to wait until the price has almost reached the English auction price. If you are successful, your opponent will wait until after the price drops below your threshold price, allowing you to win the Dutch auction without exceeding your threshold. It would seem to me that any significant divergence between the first and second auction prices is evidence specifically of this second strategy being employed.

However, "shenanigan" strategies are only viable if there is variation in what different people are willing to pay for the houses, and if it is possible to conceal one's own threshold. For example, imagine that people are bidding on a \$100 bill. There is no question that everyone's threshold is \$99.99, and everyone knows it, so there is no room for deceptive strategies, however unscrupulous the bidders may be. If the true value of the houses is well-known before the auction, then I would expect very little movement of the price in the second auctions, since the first auction should pretty much nail the true value of the house.

Edit 3: To answer the OP's specific question:

Why would you drive up the price in the first round if you could "always" pick it up in the second round for EUR 2,000 above a (much) lower price?

Imagine that they just skipped the English auction and set the Dutch auction to count down all the way to \$0. In general, I would expect more or less the same final outcome. In a sense one can consider the English auction as setting a reasonable floor price. Then, for the "real" auction (round 2), anyone whose threshold lies below the price established in round 1 can take a break and check their email, while the people still interested at that price can fight for it in an arguably more efficient manner (a single bid ends the auction).

So basically, the first round is irrelevant to the final outcome; the Dutch auction will stop at or near the top bidder's threshold price regardless of what happens in round 1. If I was a lazy bidder, I might care so little about the first round that I wouldn't even start paying attention until round 2. I wonder if any of the participants did this?