Optimal Auctions Blog

The Difference Between Clock and SMR Auctions

Posted by Mike on July 31st, 2012
The Difference Between Clock and SMR Auctions

Throughout our dealings with clients the same question always comes up - "What is the difference between a Clock auction and an SMR auction?". It's an understandably important question. Sometimes the difference between the two auction formats can be subtle for those unfamiliar with auction design. However, by using a simple apples vs. oranges comparison, the main difference between the two should become obvious, and also show you the strengths of each auction format.

It's all Apples vs. Oranges

Imagine you're a fruit farmer who has a fruit stand. You have only 2 items left, one apple and one orange. There are 4 people milling around your fruit stand ready to buy the items, but you aren't sure how much any of them will pay for the apple or the orange. Naturally, you decide to hold an auction. You will sell the two items of fruit (whole and unsliced) to the 4 bidders.

Apples for Oranges - SMR vs. Clock AuctionsEach bidder will place a different internal price on the items. Alex may LOVE apples and be willing to pay $3 for the apple. But, he may also hate oranges and wouldn't pay even a penny for it. Bob may be indifferent to both fruits and be willing to pay only 50 cents for either the apple or the orange. Carl may like apples AND oranges but he might only be willing to pay $2 for either. Doug has $2.50 in his pocket and is hungry, willing to buy either type of fruit.

You can see the auction design has influenced the overall demand curve. Because the apple and the orange are substitutes to each other, some bidders may be willing to switch from buying the apple to buying the orange when the price of the apple gets too high, and vice versa. Additionally, though apples and oranges are substitutes, they aren't identical - some bidders will place a higher value on apples than they would oranges.

If this auction would be played out, you would see Alex win the apple at $2.01, and Doug would win the orange at $2.01. Because the maximum Carl would pay was $2 for either fruit, he ended up losing both fruits to bidders who were willing to pay more.

You've just seen a perfect situation for an SMR auction!

Ideal Situations for an SMR Auction
  • Items are not divisable into smaller units. In our example, the bidders wanted the entire apple or the entire orange.
  • Items are substitutes for each other, but not identical. In our example, some bidders would switch from an apple to an orange, or vice versa, when the price of one got too high.
  • Bidders have different demand curves for the products. In our example, some bidders would pay a high price for the apple, some would only pay a low price.

Let's revisit our fruit stand example now. Suppose that you're the fruit farmer and now you only have 1 apple remaining. You are a nice farmer, but you want to maximize the amount of money you can make from this apple. You have the same 4 bidders. However, now you add one change into the auction - you will slice the apple into 6 identical slices. Further, you tell the bidders the maximum number of slices they can buy is 3.

Apple slices - SMR vs. Clock Auctions

This small change has a big change on the auction dynamics. Instead of offering a single apple that could only be won by a single bidder, you are now offering 6 identical slices of the apple, and limiting the number of slices any single bidder can win. The bidders don't care which slice they win (they are identical), they now only care about the quantity of slices they win.

The auction design has again influenced the demand curve of the product. Each item for sale (a slice of apple) is a perfect substitute for each other - this is what we call in the auction business a "commodity". The demand curve for 1 slice is exactly the same as for a different slice. The bidders don't care which individual slice they win because they are identical. In this type of auction, bidders merely bid the number of slices they are willing to buy. As the prices tick up, the number of slices they buy will start to decrease.

In this new auction, continuing our example, Alex would pay 50 cents for a slice for 3, Bob would pay 8 cents a slice, Carl would pay 33 cents a slice, and Doug would pay 42 cents a slice. As the slices become more expensive, bidders like Bob will scale back the number of slices they bid, until the point that Bob will bid 8 cents for 1 slice. When the price moves up to 9 cents a slice, Bob will drop out of the auction. Eventually, when the price reaches 34 cents a slice, Carl will drop out. That will leave Alex bidding 34 cents a slice for 3 slices, and Doug bidding 34 cents a slice for 3 slices. The auction will now end!

You've just seen a perfect situation for a Clock auction!

Ideal Situations for a Clock Auction
  • The item can be divided into smaller identical units. In our example, an apple can be sliced into 6 identical pieces.
  • Items are perfectly identical substitutes (commodities). In our example the bidders don't care which individual slice they win, only how many slices they win.
  • Bidders have 1 single demand curve for the product. In our example, each bidder has a demand curve that said as price increased, quantity demanded decreased.

Can I Have a Combination of Clock and SMR?

Yes, of course! This type of auction will pop up. Using our example from above, imagine that the fruit farmer wants to sell both his apple and his orange, and he wants to sell his apple in 6 slices, and his orange in 4 slices. As you've learned already, the apple and orange are substitutes, so that points to an SMR design, but the slices are identical to each other, and that points to a Clock design. It turns out that this type of auction is actually quite common in the real world. It's so common that our team performs these more often than any other type of auction.

For some reason, this type of auction design, a combination of the basic SMR and Clock auction formats is still called a "Clock auction" in the auction world. But, as you hopefully have learned by now, it shares designs with both the SMR and Clock auction.

How Does This Map to the Real World?

By using the apples and oranges example, you should see the difference between a Clock and SMR auction. But how exactly does this map to a real world auction situation? How about a spectrum auction, why do some auctions use an SMR while some use a Clock?

Suppose there is a spectrum auction in a small country like Barbados. The country wants to slice the spectrum into 3 slices in order to promote competition, and each slice will cover the entire country. Each slice is identical to the bidders. You should see right away that this auction design maps to a Clock auction design. (Choosing the actual slice a bidder wins can be done by random drawing or a supplement phase).

Now, let's change our example to use a big country like Brazil. The country wants to respect regional telecommunication firms, and so slices their spectrum into products like "Rio 4G", "Brasilia 4G", "Sao Paolo 4G", etc. The products in this auction are not identical, but they are subsitutes for each other (but not identical - a regional company in Rio has no interest in winning the Brasilia slice, while a national firm like Telefonica would want to win across the entire country). You should see that this auction would be best suited for an SMR auction, since each bidder has a different demand curve for each product.

The Final Wrinkle

One final thing to discuss - choosing to implement your auction as an SMR auction will never lead you down the wrong path. However, choosing to implement your auction as a Clock auction might lead you down the wrong path. In other words, if your auction design screams for a Clock auction and you instead implement it as an SMR auction, there won't be any negative consequences, and your auction will still run fine to completion. On the other hand, if your auction screams for an SMR design and you choose a Clock auction design, you will likely run into problems that prevent your auction from completing successfully.

Ultimately this means "when in doubt, choose SMR". Combining the safety of the auction design with its other beneficial feature (very easy to understand for bidders), the SMR auction design is typically the best for simple auctions for our clients.