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

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

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Are you asking why anyone takes part in the first round at all? – oks Feb 12 '13 at 19:45
@oks Except for the very first (ridiculously low) bid (to at least get collectively to the second round), I'd say that would be at least a clarifying aspect (as it is the other extreme). But it's not the question. – Keep these mind Feb 12 '13 at 19:53
Why would a person choose to bid in the second round, but not to make the same bid in the first round? I think I'm missing something. – David Speyer Feb 12 '13 at 21:16
@DavidSpeyer Perhaps because "winning" only the first round doesn't get you anything, whereas winning the second round gets you a house (for a price)? – Keep these mind Feb 13 '13 at 8:49
I've put up a related question on a highly theoretical model of this situation. – Keep these mind Feb 13 '13 at 19:14

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.

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I like it, but could you perhaps expand... Would this explanation imply that either 1) there are no single-time hopefuls (only interested in the specific house under auction) present, or 2) they are stupid? – Keep these mind Feb 13 '13 at 8:28
@Gugg: It would imply that single-time buyers who value the house exactly between the highest and next-to-highest of the regular's valuations are rare enough that it's still advantageous to the regulars as a group to keep the system running. Since they know who each other are, they can distinguish between an outsider making a rough bid and an insider defecting from the tacit agreement. The former is to be expected once in a while as a boundary condition; the latter leads to the mutual trust in the arrangement breaking down. – Henning Makholm Feb 13 '13 at 11:15
I still like it! I wonder if this explanation by invoking mutual trust/iteration could possibly still be better. We still miss half of it: Would we indeed expect to observe (significantly) different strategies* after trust has broken down (or if we are in the last iteration)? If yes, then this would strongly set this answer apart from the current other answers. – Keep these mind Feb 13 '13 at 12:05

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?

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Please bear with me. Didn't you somehow mix up willing and preferring? Imagine me wishing to participate once, since I am hypothetically only interested in buying my neighbour's house. I have a valuation of EUR 120,000 for that specific house, but I would prefer paying less. We are in round 1. Bidding seems to be stalling at EUR 90,000. (The last bidders, and all the others, are keeping silent now.) Are you suggesting that it is somehow rational for me to start participating in round 1 and bid EUR 91,000? Or should I keep silent and, if I get the chance, call in round 2 at EUR 92,500? – Keep these mind Feb 13 '13 at 8:15
@Gugg: I am suggesting that you should bid in round 1. If you adopt the strategy you're suggesting, it is possible that you'll be undercut by someone with a lower maximum price than yours. In your example, imagine there's someone else out there who values the house at EUR100,000; then they might conceivably beat you out by placing a Dutch bid of anywhere from EUR93,000 to EUR100,000. So by not bidding the English auction up until they're priced out, you've left EUR20,000 on the table. – Micah Feb 13 '13 at 8:40
Let's continue the example, if you don't mind. Assume that all, except me, follow your strategy and that the third-highest valuation is EUR 89,000. Bidding in round one will then stop at give or take EUR 90,000. Why would the holder of the (second-highest valuation) EUR 100,000 valuation, bid at say EUR 93,000 in the second round if he's thinking like you are? On the other hand, I take it that I have to be concerned only about those that are not planning/willing to bid up to their valuation in round 1. – Keep these mind Feb 13 '13 at 10:20
@Gugg: Well, for one thing, your EUR2500 increment is arbitrary and therefore a little suspicious. The fact that someone could beat me out by adopting a minor variant of your strategy -- namely "keep silent, and, if I get the chance, call in round 2 at EUR92500+$\epsilon$" -- makes me highly leery of that strategy. – Micah Feb 13 '13 at 15:44
@Gugg: It's true that guy #2 has nothing to gain by matching my EUR90,000 bid in round 1. But he doesn't know that unless he knows my valuation is significantly higher than his! And if the players know each other's valuations, the game becomes trivial. – Micah Feb 13 '13 at 15:51

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.

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I noticed that the highest bidder of the first round is allowed to bid (higher) in the second round as well. I'm not sure if you did take that into account. What did you mean by: "I should have saved my breath the first time"? Is that a (rational) strategy? – Keep these mind Feb 13 '13 at 14:00
@Gugg: If I bid in the second round, I eliminate any effect of winning the first. If I can bid the second round at a point I accept, the only new information is that nobody else bid yet. So I think the strategy of bid x in the first round, then if I win, bid y in the second is dominated by don't bid in the first round, then bid y in the second. Same result, less effort. – Ross Millikan Feb 13 '13 at 14:10
I am wondering about the possible common knowledge concerning the small spread of (then not so) private values. Given the uncertainty surrounding some of the houses (not being able to preview, evictions pending, unknown tenants, etc.), the spread should at least reflect the spread in risk-aversity. But if they are not "sophisticated" in this way (or not risk-averse), perhaps they are sophisticated in another way: could they be using the same source/model/authority/meeting(!) for their private values? Could this explain things (a little better)? – Keep these mind Feb 14 '13 at 7:08

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 ;-)

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Well, your guess is at least as good as mine. I like how you seamlessly moved from bidding to betting :). So, in brief, your explanation revolves around... punishment? – Keep these mind Feb 13 '13 at 10:29
Not really. I am just saying that the usual $\frac{n-1}{n}$ doesn't apply anymore, if you wan't to win, you have to bet much closer to your real valuation (because of the estimates). This helps to make $v_{max}$ the winner not some lucky guy who went against the tide and bet $\frac{2n-1}{2n}$. Of course, some form of punishment might be there (those are real people, right?), but I don't think it is the main motivation. – dtldarek Feb 13 '13 at 10:41
I think $\frac{n-1}nv_{\mathrm{max}}$ is under the assumption that the valuations are independently uniformly distributed? That assumption might not apply in this case. – joriki Feb 13 '13 at 20:26
@joriki Indeed it doesn't apply. I think it is one of the main reasons for the joint English-Dutch auction, see my previous comment. – dtldarek Feb 13 '13 at 20:45

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?

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I think that with your edit you hit some nail on the head. You should see this crowd of traders, brokers and bankers. They practically define shenaniganism. Game theory should apply. You would expect to find evidence of this in their strategies, unless of course 1) the mechanism is "robust" to sharp practice, or 2) they are rigging the game in other, yet unobserved, ways. (But I wouldn't call participating only in round 2 unethical.) – Keep these mind Feb 13 '13 at 9:51
I responded to your comment with a second edit, since it was too long for a comment. – Ryan Thompson Feb 14 '13 at 0:17
Thanks. "I wonder if any of the participants did this?" I think I observed that some of the final winners did not participate in round 1. They were regulars. And they were within EUR 3,000 (I initially made a mistake with regards to the EUR 2,000) of the round 1 floor. Given that I'd assume that the private values are actually spread quite wide, that is surprising. But maybe I simply lack insight in how they establish these private values in the first place. Do they all have the same valuation model? To me, they don't look like model people. Do they all listen to an "oracle" or authority? – Keep these mind Feb 14 '13 at 6:54
Well, I assume these people are not in the market for houses to live in; they are buying houses in order to fix them up and sell them, right? So it's very possible that their valuation model is based on the price they can get for the house (minus refurbishment costs), which might be an easy number to estimate, or might be determined by some "list price" or something that is acting as an "oracle". – Ryan Thompson Feb 14 '13 at 16:52
Also, if you knew for certain that you were the only person to sit out the first round, then you could be confident that the first-round price represented the maximum of all your opponents' price thresholds, and you could safely buy the house for just a bit more than that, regardless of how much higher you would have been willing to pay. If you don't know this for certain, you can still take a calculated risk that it might be so and have a reasonable chance to win the house for a price under your threshold, which might make it a viable long-term strategy. – Ryan Thompson Feb 14 '13 at 16:55