Auction Theory

Like the rest of you, I’ve been thinking about auctions and auction theory because nothing pairs better with a beautiful weekend morning than considering the efficiency of asset pricing mechanisms and writing about it. I’m sure you’ll agree.

(I asked ChatGPT to draw a picture to represent the opening sentence. This might be entirely too accurate… minus the suit and tie… and I’m not blue. But money is growing on the tree.)

Auctions are purported to efficiently balance speed and price when selling assets, but they may not deliver price discovery as effectively as we assume. This article challenges the idea that auctions maximize the selling price and explores the theoretical price auctions deliver.

Background

I have personal experience with several different types of auctions: live auctions of random stuff (including livestock), M&A auctions, and real estate auctions.

Triple story time…

1 – Live Auctions

When I was in elementary school, my parents would occasionally decide that nothing said “family fun” quite like allocating a Saturday evening to our local auction in Catoosa, Oklahoma, galactic headquarters of small towns.

Consequently, I attended quite a few American style auctions, the kind where most people are not entirely sure how much they bid because the auctioneer sounded like an AK-47 trying to count. The rapid fire, melodic, staccato babble occasionally sounded like recognizable numbers… maybe.

There’s a process to auctions. In the pre-auction phase, you have an opportunity to walk around and view the items for sale, basically browsing and tire kicking. After that, you take a seat as items appear out front, number-babbling begins, and bidding starts.

If you are the winning bidder, you settle payment at the register and haul whatever you bought home with you. Some pre-planning might be required for larger items.

I distinctly remember two purchases at the Catoosa auction: a foosball table and a dinner bell.

We were in the pre-auction phase when I said, “Dad, check this out,” as I walked by a foosball table.

“Hmm. Looks like it used to take coins, but that mechanism has been removed. But otherwise, everything seems to work,” Dad replied.

Kind of a cool item, but we moved on to inspect other stuff.

Fast forward to bidding…

The order in which the items were presented at the Catoosa auction seemed as random as the items themselves. During the bidding, the foosball table eventually rolled out and, to my surprise, Dad raised his sign showing our bidder number. Surprise! There were only a few back-and-forth bids until Dad “won” the foosball table for $53. This was the early 80’s so this amount equates to about $200, inflation adjusted to 2024-dollars.

We had a lot of fun playing foosball over the years. In fact, we played so much that I’m fairly confident I can win playing two against one, most of the time. I wouldn’t stand a chance against a real foosball gangster, but against the average citizen, no problem.

The other item my parents bought at the auction was an old brass dinner bell from 1878, pictured below.

I know, I should have polished it before taking the picture.

The inscription reads: GWRR Co. 1878

GWRR stands for Great Western Railroad Company and if I’m doing my math right, it’s about 10 million years old!

This bell might have been used at the train station to signal an inbound or departing train. Alternatively, the railroad crew’s cook might have used the bell exactly as my mom used it for many years thereafter – to signal when dinner was ready. We could hear this bell from the back of the pasture. It’s loud and has a beautiful tonality.

After we had kids of our own, this dinner bell was bequeathed to my household. My wife (Sofie) then continued the ritual of ringing the dinner bell, which is what my kids heard growing up, but on a cul-de-sac in Austin, TX. The neighbors frequently knew when dinner was ready at our house. We still give it a soft ding or two when everyone is in the house, usually preceded by the phrase, “plug your ears” for anyone already in the kitchen. I literally did this yesterday and said those exact words. Nostalgic.

Anyway, this was my early childhood experience with auctions, but not my last auction experience.

2 – M&A Auctions

Fast forward. I would later work as an investment banker advising clients on mergers & acquisitions. Preferably, we would sell our client’s company in an auction process. The idea is to get all the potentially interested buyers to submit bids for the company on the same day.

Of course, buyers would rather not be part of an auction process. This is partly because it feels like they might pay more in a competitive bidding process, and partly because an auction just doesn’t make buyers feel quite as special. Buyers much prefer to be the only interested party in purchasing the company. In this instance, feeling special is important, and opportunistic, and profitable.

However, investment bankers know,

If you only have one buyer, the buyer has you.¹

And the related saying:

You don’t need two buyers in an auction process. You just need one buyer who thinks there are two.²

A friend of mine invited me to lunch years ago (measured in decades) to discuss selling the company where he worked.

“Hey Andy, the company I work for is considering an exit. I’ve been put in charge of the deal. Can I bring you in for a short consulting assignment to talk to us about the process?” he asked.

It was a relatively small company, and I was happy to share some knowledge to help a friend.

We had some preliminary discussions to better understand what they were trying to accomplish. I also reviewed the financial statements and listened to the backstory.

After some thought, I had a $5 million ballpark valuation for the company in my mind.

My friend continued, “The owner, my direct boss, would like to get $20 million for the company.”

“OK… uhh… I thought $5 million might be where we would land, given the company’s current revenue, profitability, and growth prospects. $20 million is way up there,” I replied.

I should note, it’s not unusual for company owners to think their baby is beautiful, but this seller’s expectations presented a large discrepancy from what I believed would be a more realistic market pricing.

“Well, the company might be worth $5 million for the current cash flow it produces, but our team provides a solution to a billion-dollar problem for a much larger, publicly traded company,” my friend countered.

I thought, but did not say, OK, well. Good luck with that. Knowing that a deal this small is just a rounding error for a multi-billion dollar, publicly listed company. It’s very difficult to get their attention for a deal this size.

I replied, “I normally give most M&A deals about a 40% – 50% chance of a successful exit, even with reasonable price and terms, when everything goes smoothly. 5% – 10% if the expectation is to sell to a pre-identified target buyer. It just doesn’t usually happen…that the seller’s idea of the buyer is the actual buyer, or the best buyer.”

I continued, “The probability that this massive publicly traded company will be the ultimate buyer AND pay $20 million, 4x the realistic market valuation, is very low. I’d estimate less than a 5% chance of closing this deal with this buyer, at this valuation, given the special circumstances surrounding the deal.”

“We’ve already had initial contact with the target buyer and have had some preliminary conversations with their tech team.”

“I don’t mean to sound pessimistic. It’s a great business. Truly. I’m just trying to set realistic expectations for you and the leadership team,” I cautioned.

Apparently, the company did have a solution to a billion-dollar problem. The large publicly traded company (the buyer) could either try to build the needed service in-house and spend the next 24 months doing it, meanwhile leaking tons of cash from the fundamental business problem they were trying to solve (I’m being intentionally vague here for confidentiality reasons)… or, the public company could buy this much smaller company and solve their large problem in 6-to-9 months.

Fast forward some months. I heard back from my friend.

“The company sold for $20 million to [the large corporate buyer].”

So, this is a story where I was wrong, and there are a few lessons to coax from it.

• Valuation is unique to each buyer. This is true for a thingy sold at a small-town auction, for a house, and for a company.
• Valuations can get unexpectedly high with the right buyer. If there’s a large incentive, like solving a huge problem that is much larger than the item for sale (at least in the mind of the buyer), then the cash flow the company produces can be a secondary factor in valuation. The primary driver becomes cost avoidance, or speed to market, or another similar strategic rationale.
• A seller can act as a ghost bidder #2 if a viable top bidder #1 has already been identified… and if the seller is armed with sufficient insight into the buyer’s mindset, incentives, and fundamental motivations… and if the seller is sufficiently stubborn (and more than a little gutsy)… and if the seller is willing to walk away from the deal. We’ll come back to this point.

“But this isn’t an auction story,” you say to yourself.

I know. I realized that after I wrote it, and I didn’t feel like editing it out. The irony is, I picked an unusual M&A deal story to tell here, an example of the opposite of what this blog post is about… namely auctions. So, uh, think of it as a bonus. I’ll figure out how to tie it all together below.

3 – Real Estate Auctions

Most homes in Sweden are sold in a modern auction process.

When a house comes up for sale, it’s posted on an internet marketplace, much like Zillow here in the U.S. (Click the link. It’s in Swedish, but I have set the filters to show some beautiful places. Look at the pictures and appreciate the beauty of the country.)

In-person showings follow a few weeks later, often on a weekend, and likely a second showing the weekend after that. Once again, this is the browsing and tire kicking phase. During this time, buyers register to bid on the house with the sell-side realtor. This usually requires some proof-of-funds, or a letter from the bank showing mortgage qualifications.

Bidding starts shortly after the second open house, often the next day or two.

Each bidder is assigned a number (#1, #2, #3, etc., in the order of bidder registration). While you do not know who the other bidders are, you do know their bidder number. Consequently, you can track bids online, in near real-time, and see which bidder number made the latest bid (plus you can see the chronological history of bids by timestamp, bidder #, and amount). Except for the actual bidders’ names, it’s all quite transparent.

As a bidder, a lot of thought goes into when to bid, when to wait/pause/delay a bid, how much to bid above the previous bid (the minimum increment or a large jump… both signal intent), or if to bid again at all. In a perfect world, you establish the maximum you are willing to pay BEFORE the auction begins. That’s what we did… because we are conservative, frugal, and analytical and not prone to fall into the hype of bidding for something in a live auction.

I said to my wife, “Sofie, I’ve looked at all the comparable transactions in the area. Here’s the spreadsheet with all the supporting recent transaction data. I think the realistic market price should therefore land around $X.”

“However,” I continued, “given the proximity of the house to your parents and siblings, the location is a premium for us. What do you think about bidding up to $Y?”

“Sounds good, but we have to have a hard stop at $Y and not get swept up in the bidding process,” Sofie replied.

“Exactly.”

Once bidding started, we had a strategy of bidding often and quickly after the previous bid, communicating to other bidders our earnest intent to win the auction.

“Sofie, the last bid by bidder #4 hit our max price exactly.”

“Oh bummer.”

“Well, I think we could justify one more increment higher, in case that nice round number was also their max bid amount,” I suggested.

“Are you sure?”

“Yeah, let’s put in one more.”

“OK, let’s try it, but just this one increment,” Sofie said.

“Cool. Let’s do it.”

Yeah, I know, I wasn’t expecting that either.

Basically, we just broke the hard rule of not exceeding our predetermined max bid price shortly after agreeing on it. We are normally disciplined, but we really liked the house and the location, which is perhaps another way of saying, the auction-hype got us. So much for “conservative, frugal and analytical”.

A little while after we bid too high, I said, “Hey Sofie, looks like bidder #4 came in above us again. Should we put in one more bid?”

“Well, that’s uhh, that’s getting pretty high now,” Sofie cautioned.

“I know, but it’s a great place,” I said.

You can see this was clearly all Sofie’s fault.

We agreed to take a moment to think about it, which we did…

“OK, the NEW, new highest we will bid is [$Z]. Let’s put in one last bid.”

Emphasis on “last”.

In the meantime, bidder #2 submitted a bid above the new max number we had in mind. Fortunately, that settled it. We did not bid on that place again and accepted that house would not be for us.

Sometimes the outcomes we do not want are the best for us.

The last two bidders continued to bid up the final price several more times. The house sold for considerably more than we thought it would or should, based on the comps. Apparently, we weren’t the only ones caught up in the auction buying frenzy.

Ultimately, we bid on three houses in Sweden. For the first two, the winner’s curse³ fell to someone else. On the third one, it fell to us, fortunately.⁴ Did we overpay on the third try? Hard to say. Perhaps. But it doesn’t matter, because we love the place. So, it was worth it to us. This is the case where we were likely one of the “best” bidders for the house in that it had value to us in excess of the value it presented to others.

Auction Theory

These auction-related memories from my childhood, my profession life, and our home purchase had me contemplating auction theory and the mechanics of the auction process. Specifically, I was considering the question: What makes for an ideal auction?

Let’s discuss.⁵

Auction theory is the study of bidding strategies and outcomes in auction markets. It examines how auctions influence participant behavior, transaction efficiency, and prices.

Behavior – as we saw in my story about bidding on the house, behavior is an important component of auction theory. Of particular interest is how our behavior might change and lead us to bid more than we would have otherwise. The key strategy here is, you should NOT view an auction as a competition, especially not one in which you strive to win as a bidder (hence the winner’s curse). Winning the bid does not mean you have won… just like folding a poker hand does not mean you have lost.

Efficiency – auctions can provide an efficient method to dispose of an asset quickly, but it might be at the expense of finding the best buyers. Therein lies a potential trade-off. However, sometimes the speed of the disposal of an asset is an important factor that might weigh heavily on selling decisions, or even trump the price of the asset.

Price – auction theory also examines the efficiency of allocation… that is, whether the item ends up with the bidder who values it the most. In the case of the M&A deal I described, there was only one official bidder, the large corporation, (and hence not really a formal auction). However, this buyer was likely indeed the entity that valued the company and its assets the most. Including this top bidder in the sales process yielded a considerably higher valuation.

Most texts on auction theory state something like, “The maximum price is often set by the bidder who values the item the most.” This is the part I’d like to discuss in more detail. But first, let’s set up our discussion about a hypothetical auction process with some basic assumptions…

Assumptions

Much like game theory makes simplifying assumptions, we will here as well, to reduce the thought exercise into something more manageable. Consequently, we will assume:

• Each bidder plays a smart auction strategy. Meaning, each bidder begins the auction with their theoretical maximum price they are willing to pay for the item being sold – a thing, a house, a business… and, more importantly,
• Each bidder stops bidding at their predefined max price, (unlike Sofie and I bidding on houses).

Given These Assumptions…

• The max price paid for the thing for sale in an auction is NOT what the top bidder is willing to pay, contrary to what people think.
• The max auction price achieved is the smallest bidding increment above the 2^nd highest bidder’s max price.
• Consequently, it is not the top bidder who sets the max price (only their presence). The max price is determined by bidder #2.
• Therefore, the only bidders that really matter are bidder #1 and bidder #2 (defined as the two highest possible bidders based on their max predetermined price they were willing to pay).

Implications

• The problem is, by design, no one knows who bidder #1 and bidder #2 are until the auction has concluded.
• The auctioneer (or the intermediary, real estate agent, or investment banker) is then tasked with finding the “best” possible bidders #1 and #2 to attend the auction and to encourage them to bid eagerly by presenting the asset in the best possible light… and sometimes by hyping them up during the auction itself.
• To accomplish this, often the idea is to get more bidders. The logic being: more bidders equates to a higher probability of including a better bidder #1 and bidder #2. This seems rational, but only works to increase the probability of including the best bidders. It does not ensure it.
• It is entirely possible that an auction with ten bidders that concludes in a final price and a sale was not a successful auction. Of course, the investment banker would say, “We had 10 concurrent bidders for the company. We ran the auction and thereby established market price for the company. A great process.”
• But what if…

CASE #1 – the auction was missing a strong bidder #1.

In this case, the final price was sealed by bidder #2, the faux-bidder #1, and the final price was actually determined by bidder #3, acting as bidder #2. Thus, a lower than market price was established, and the company sold below true market value… because bidder #1 was not present during the bidding process.

CASE #2 – the auction was missing a strong bidder #2.

In this case, bidder #1 was present and was perhaps even willing to pay considerably more, but the auction price capped out just incrementally above bidder #3’s max price. Again, even though bidder #1 was present, bidder #3 was a faux bidder #2.

So, we have established that, without a strong bidder #1 AND a strong bidder #2, the item for sale caps out at the bidder #3’s max price. You can see how we can extrapolate this logic further, to the case where there is only bidder #1 and bidder #8, for example. Then the final price is just incrementally above bidder #8’s max price. We missed bidders #2 through #7.

These are all cases of suboptimal auctions, but no one knows they were suboptimal (at least not at that moment). Perhaps later, a subsequent bidder-after-the-fact was identified. This usually sounds like, “Why didn’t you tell me you were selling? I would have been very interested and would have paid 20% more.” Oops. Too late.

So, while auctions can be efficient, the speed of the process might neglect finding the best possible top two bidders.

Auction Price Optimization

As we can see, it is vital to actively find the best bidders #1 and #2 to avoid a failed or sub-optimal auction.

How do we ensure that we include bidders #1 & #2 in an auction process?

• More Bidders. Certainly, more bidders increase the probability of a successful auction. But more importantly, we need…
• Better Bidders. Investment bankers, real estate agents, brokers, intermediaries and auction houses should strive to include bidders with a significant interest in the target item for sale and a strong strategic rationale to purchase it (even if that reason is “because it would be fun to watch the kids enjoy playing foosball”). This is only uncovered through significant pre-auction-research, outreach, and likely a large preexisting buyer network.

In the case of the M&A deal I described above, this was not an auction, because there was only one buyer in the process. However, the seller effectively acted as bidder #2 in the sales process, because he could always just not sell. The owner was in a position where he was not compelled to sell… just willing, given the unique circumstances.

From the perspective of the corporate bidder, this was effectively the same as having a second buyer bidding against them, in that the outcome would be identical.… that they would not buy the company and would still have to deal with the expensive internal problem themselves.

Had the large corporate buyer acted smarter in the process, they would have held some of the strategic rationale for the acquisition to themselves and carried a tactical advantage in the form of information asymmetry (between the buyer and the seller). However, because the buy-side team overshared, the seller understood the extreme value to the buyer and knew they could demand a significant premium. In this case, there was symmetry in information (at least on this key point) and the seller took advantage of it.

This M&A deal presents an example where an auction might not have brought the best outcome for the seller. They might not have identified this particular corporate buyer (perhaps the timing was off relative to a scheduled auction timetable). Further, by not having to sell (in an auction), the seller was well positioned to A) have the best buyer discover them; and B) act as their own faux bidder #2. Both of these terms drove an increased valuation for the exit.

Conclusion

The efficiency and success of an auction depend on securing the best possible bidders, particularly the top two. While increasing the number of bidders can enhance auction outcomes, finding well-suited, strategically motivated participants is crucial. In some cases, such as the M&A example, alternative approaches to auctions may lead to better results by ensuring the best potential buyer is discovered, while the seller retains a strong negotiating position.

Now, go bid on one of these houses in Sweden and see if you can stick to your original max price!

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Have an auction story of your own? Share it in the comments below.

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FOOTNOTES:

1. I first heard this from Phil Wilhite.
2. I later heard this corollary from Larry Schumann, who also worked with Phil. Both Larry and Phil were great mentors to me. We still stay in touch and meet occasionally for lunch.
3. Winner’s curse” is a well-known theory about auctions. If you win, by definition, you were willing to pay more than everyone else. Perhaps you overpaid.
4. “Winner’s Curse” isn’t always a curse. Every buyer has an idea of the value of the auctioned item, specific to them. It could be that the auction winner underpaid for the item relative to the value it might add to them or their company… or the perceived value to their life. Sometimes the winning bidder in an auction is the winner because the price they paid for the item (or land, or business, or whatever) was lower than the value of that item to them. At least, that is what we tell ourselves after we overpay for something at an auction.
5. This is likely not something new, but it’s new to me, and I like the thought logic I have developed here, which was probably originally conceptualized 5,000 years ago. I mean, in the grand scheme of the cosmos, that’s still fairly recent, right? I’m not going to research this for fear I will in fact prove that I am 5,000 years late to the party. Perhaps everyone already knows what I am about to write on auction theory. If so, you can add to the comments section, “I already knew all that.” Or, alternatively, “I didn’t know all that, but now I do, and I still don’t care.” At least I will know who reads the footnotes.