[based on the ver­sion of 18 July 2004 from the old blog site]

An idea came to me some days back. For the most part, it was inspired by my deep and carefully-​​considered abhor­rence of eBay’s recent “mar­ket­ing moves”, but it’s also (I think) a neat new idea.

I want to share it. I’ve seri­ously con­sid­ered patent­ing it. Instead, I’m just going to throw it out there into the realm of pub­lic dis­course — and prior art. If you think it’s a good idea, please do take a minute to read the Cre­ative Com­mons license word­ing down there in the bot­tom right of the page — it’s important.

Back­ground

It’s dif­fi­cult even in the best cir­cum­stances for col­lectibles and one-​​of-​​a-​​kind items to sell at a fair price. I’m talk­ing about things that aren’t com­modi­ties. Things for which there is lit­tle or no com­pe­ti­tion. To sum­ma­rize a whole lot of advanced mar­ket­ing research and com­pli­cated eco­nom­ics in one par­tial sen­tence: the prob­lem lies in the spar­sity of poten­tial cus­tomers, the diver­sity of rea­sons they might want the thing, and the dif­fi­culty of let­ting the right peo­ple know it’s for sale. And some other places, too.

In real-​​life mar­kets, whether they’re Yan­kee auc­tions or dou­ble auc­tions (stock) or fixed-​​price store­fronts, non-​​commodity items are (I’ll declare with­out schol­arly jus­ti­fi­ca­tion) a typ­i­cally under­priced. Read about the Rev­enue Equiv­a­lence The­o­rem if you want to under­stand it the way clas­si­cal eco­nom­ics approaches this, but real­ize that this impor­tant result depends upon assump­tions like mul­ti­ple peo­ple inter­ested in each item are present at the sale and every poten­tial bid­der is there for the full dura­tion of the sale. Go buy and sell things like roadmaps and estate jew­elry and antique horse­shoes — or just attend two real-​​life estate auc­tions — if you want to really under­stand how the “crowd” affects the sale price of items.

Here’s the kicker: Online, it can be worse.

All that hype they (we) were toss­ing around dur­ing the dot­com rev­o­lu­tion was simul­ta­ne­ously true and false. There are more peo­ple using the Inter­net to look at auc­tion sales than there are attend­ing any one seller’s phys­i­cal shopfront or real-​​world auc­tion: the extra peo­ple are out there. So based on that alone, the odds seem to be higher that some­body who’s inter­ested in your exact item might find it. But in the same period, it has become so incred­i­bly easy to cre­ate an online sale that there are more things for sale, mak­ing it far, far harder for these more numer­ous cus­tomers to find your par­tic­u­lar stuff. Tragedy, meet Com­mons. Com­mons, Tragedy.

If there aren’t enough peo­ple see­ing the offer­ing, then there surely is less chance of an up-​​bid in an auc­tion for­mat sale. Keep in mind that both auc­tion and fixed-​​price sales typ­i­cally need to be seen by mul­ti­ple inter­ested par­ties before the price approaches a fair value: Auc­tion pric­ing depends on up-​​bids to dis­cover prices, and sell­ers using fixed price sales need to be able to adjust prices upwards between sales to dis­cover fair price. In either case, the time-​​scale needed to wait until they hap­pen by with their money in their hot lit­tle hands is longer than the time the price might nor­mally change.

In brief: unfind­able offer­ings com­mand decreased prices.

It’s inter­est­ing to con­sider that eBay’s and Yahoo’s Yankee-​​style auc­tions typ­i­cally last for seven to ten days. Orig­i­nally, when these venues were new and there were far fewer items on offer than there are today, that was enough time for mul­ti­ple inter­ested bid­ders to see the sale and decide whether to bid or not. Now that there is an over­whelm­ing assort­ment of offer­ings, and find­abil­ity is gone, the 7-​​day auc­tion is arguably no bet­ter than a 1-​​day auc­tion, and just a cash cow for eBay (who charge by the list­ing).
Brows­ing eBay cat­e­gories in which there are a mix of com­modi­ties and col­lectibles, such as Books, you’ll see a strange dichotomy: There are hun­dreds of copies of a com­mod­ity best­seller like Cold Moun­tain on offer, and inso­far as there are suf­fi­cient buy­ers to gen­er­ate demand, the mar­ket is liq­uid and fair pric­ing is active — you can see mul­ti­ple bids on many of the books, and the final prices are very sim­i­lar for sim­i­lar quality.

But look at the anti­quar­ian books, the “col­lectible” books, each much scarcer than a com­mod­ity book. Even though the col­lectibles dom­i­nate eBay’s list­ings in aggre­gate, you will see that very few sell, and those that do typ­i­cally sell with one bid.

There’s no up-​​bidding for col­lectibles, even though online sales are sup­pos­edly made for these items. I can think of at least two ways to inter­pret this. One is that the seller has set the start­ing bid too high for the mar­ket to sup­port — but the $3.99 I pay on eBay these days for a truly rare old book doesn’t strike me as over­priced, even if it’s in rough con­di­tion. The other, more rea­son­able inter­pre­ta­tion is that there are too many sales com­pet­ing for the lim­ited atten­tion of the bid­ders. They sim­ply don’t encounter the sales in which they would be interested.

Illiq­uid­ity.

And as eBay and the other major con­sol­i­dated venues con­tinue to dom­i­nate, I can’t see how the sit­u­a­tion can improve for sell­ers, and as a con­se­quence for the cen­tral­ized venues. Com­modi­ties will sell at fair prices with mul­ti­ple bid­ders, sim­ply because even the most inex­pert cus­tomer can’t swing a cat with­out hit­ting one. Search works. But the spe­cial­ized items like antiques and col­lectibles are lost against the back­ground of the com­modi­ties, and lost among one another.

Peo­ple don’t have time to find things.
What is a Ratchet Auction?

Some days ago I wrote about Dutch (descend­ing) auc­tions, and pro­posed the notion of the Drunkard’s Auc­tion, in which the price makes a ran­dom walk up or down each tick, where the ear­li­est, high­est offer match­ing the cur­rent price is the clos­ing price.

I like the Drunkard’s Auc­tion for­mat because unlike the more com­mon Yan­kee (increas­ing) auc­tion or even the tra­di­tional Dutch auc­tion, it never ends until some­body makes an offer. If nobody has come along, it may wan­der on in its ran­dom walk, vis­it­ing all pos­si­ble prices even­tu­ally. Even when some­body makes an offer at a fixed price, it may still take some time before the walk matches that price. That’s a good thing, I’ll argue, when you’re offer­ing an item a shal­low mar­ket like collectibles.

That said, it has some flaws. It’s ran­dom. If you sam­ple the price at ran­dom, it tends to sit in the mid­dle of the spec­i­fied range.

In response, I’ve con­cocted this:

Sup­pose the seller has an item they want to offer in an online sale, but because it is unusual (an antique or col­lectible) they have (a) a poor idea of a fair fixed price that will not tie it up in their inven­tory, and (b) no expec­ta­tion that suf­fi­cient audi­ence will be present dur­ing the course of a limited-​​time increas­ing auc­tion to drive the price up to a fair one.

The seller ini­tially sets sev­eral para­me­ters defin­ing the sale’s price dynamics:

• The max­i­mum price is the start­ing price at which the lot will be offered.
• The min­i­mum price is the low­est price the seller is will­ing to accept for the lot.
• The dis­count incre­ment is the amount the price will typ­i­cally drop between two steps of the sale.
• The price per­sis­tence is the length of time a price is in effect before it changes again automatically.
• The ratchet prob­a­bil­ity is the chance that the price will jump up rather than drop­ping down by the dis­count increment
• The resid­ual dis­count deter­mines the amount of dis­count remain­ing when the price ratch­ets up.

(Does this sound like a lot to jug­gle? As it turns out, I sus­pect that many may be set to default val­ues, leav­ing only the max­i­mum price, min­i­mum price and price per­sis­tence as things that might be set by the less con­trol­ling seller.)

The lot is offered for sale at the max­i­mum price ini­tially. Peri­od­i­cally there­after, at fixed times deter­mined by the price per­sis­tence, there is a ran­dom change in the price. For a ratchet prob­a­bil­ity p, there is a prob­a­bil­ity (1–p) that the dis­count will increase (that is, the price will decrease) by the fixed amount of the dis­count incre­ment, and a prob­a­bil­ity p that all but the resid­ual dis­count will dis­ap­pear.

Finally, if the price is so low that the next dis­count would drop it below the min­i­mum price, then it will instead revert to the max­i­mum price (wrap around).

Poten­tial cus­tomers have two options: They may buy the item at the cur­rent asked price. Or they can make an offer, a pub­lic promise to buy the item when the price crosses a spec­i­fied price level.

Let’s play with an exam­ple. Sup­pose the max­i­mum price is $100, the min­i­mum price is $10, the dis­count incre­ment is $1, the price per­sis­tence is 1 hour, the ratchet prob­a­bil­ity is 3% and the resid­ual dis­count is ¹⁄₆. The online sale starts at a price of $100, and every hour there­after there’s a 97% chance that it will drop by another dol­lar and a 3% chance that it will jump back up ⁵⁄₆ of the way to $100. Say at one point it’s at $64: at the end of the hour, it will either drop to $63 or jump up to $94. If some­body comes along and buys the item out­right before the end of the hour, they pay $64; if they make an offer at $63 or $63.99, then they have a 97% chance of win­ning (assum­ing there are no other offers that pre­cede theirs, or are for higher bids). If the price should hap­pen to ratchet up, then their offer to buy at that price stands until they change or can­cel it. And if nobody comes along, and the price drops to say $10.12, then the next time the price changes it will either jump all the way back to $100 (97% chance) or it will ratchet back up to some­where less than that (3% chance).

Now, I’ll just state with­out detailed sup­port­ing argu­ment that a suc­cess­ful web-​​based sale using a Ratchet Auc­tion will depend not merely on the tra­di­tional infor­ma­tion sup­plied by auc­tion sites — pic­tures, descrip­tion, con­di­tion, cur­rent price and the like — but also will require that the exact prob­a­bil­i­ties of prices in the near future, and bid­der inter­est in the item are disclosed.

So let’s imag­ine that for each auc­tion item there is a lit­tle time-​​series graph show­ing the price over the recent past. This graph is anno­tated very clearly to indi­cate the exact time that the price will next change, and what the val­ues will be. It is anno­tated to show the web page views for the auc­tion as lit­tle tick-​​marks along the time axis. It is also anno­tated with a hor­i­zon­tal line show­ing every open offer, start­ing at the time it was logged, and at the price offered. Like this:

A graph rather like this one is shown to any­body view­ing the sale web page. It shows the price, the page views, and the offers. It shows the community’s inter­est in the item, and the tim­ing and prices of the offers are sig­nals to the seller about the gen­eral mar­ket for the offering.

The price time-​​series is that lit­tle stair-​​stepping line, which steps down (likely) or ratch­ets back up (rarely) every tick of the clock — for­ever, if nobody ever buys the damned thing. Every time any­body views the page, an indi­ca­tor is added to the graph (those rather inad­e­quate lit­tle blue ticks along the bot­tom of the graph are sup­posed to rep­re­sent that). So peo­ple know how many oth­ers are watch­ing. If any­body wants to buy the item at the cur­rent price, they can — in our exam­ple, nobody has done so. Instead, a num­ber of peo­ple have made offers, indi­cated by those broad hor­i­zon­tal lines. As soon as any user enters an offer, every­body gets to see it. When­ever any offer is crossed by the price, that per­son wins (the green offer line is the win­ner, in this case).

I’ve tried to indi­cate a lit­tle of what I think might hap­pen in this car­toon: First, that offers can be can­celed or changed by the bid­ders. Sec­ond, that low­ball offers (like that long line low on the left) will take for­ever to close. Third, that bid­ding wars and up-​​bidding can occur here just as in a Yan­kee auc­tion (wit­ness the lit­tle lad­der of offers in the mid­dle). Fourth, that the past doesn’t mat­ter — an offer that is expired or changed is no longer bind­ing, as is the case with the per­son who made an offer of about $65 between steps 50–80; even though the price sub­se­quently drops below that offer, it’s been can­celed or moved, and so they don’t win.

That’s it. The sale will con­tinue adjust­ing the price with no inter­ven­tion from the seller. Some small amount of web-​​based infra­struc­ture would be needed to update the graphs and keep track of and report the offers. At some point — when­ever prospec­tive cus­tomers hap­pen to come by — they will buy the item out­right or make an offer. As noted above, low­ball bids will take a long time for the price to reach that level, and there’s a sig­nif­i­cant risk that some more rea­son­able per­son will come along and buy the item at a higher price.

There’s a lot of tun­ing that one can do, too. You might imag­ine, given the num­bers I’ve used here ($100 max, $10 min, $1 incre­ment, ¹⁄₆ resid­ual, 3% ratchet prob­a­bil­ity) that the price will spend a long time way down low. Nope:

This is a his­togram of prices seen in 10000 steps of the same time-​​series used in the pre­vi­ous fig­ure. The red line indi­cates the mean price over time — some­where up around $72. Coun­ter­in­tu­itive, after look­ing at the prices in the first fig­ure? Here’s a hypoth­e­sis for some nice empir­i­cal econ­o­mist to test in the future: I think that these simple-​​seeming down­ward trends over­whelm­ingly trig­ger our instincts about momen­tum, trick­ing us into think­ing the price is headed for $0 every time it con­tin­ues on down for a while.

Here are a few more steps (500) — trace along and make a pre­dic­tion, based on this sam­ple, of the aver­age price. I betcha you’re waaaaayyyy under­es­ti­mat­ing it. I know I do. If you were pre­sented with this graph, and you actu­ally wanted to bid on the item, what would you bid? How ratio­nal are you feelin’, punk?

No, wait — it gets bet­ter with more trans­parency. The auc­tion list­ing should not only fully dis­close the his­tor­i­cal prices, the page views, and the tim­ing and prices of offers, but should also explic­itly state the prob­a­bil­i­ties and the pos­si­ble prices in the next tick. As in “there is a 3% chance the price will be $50, and a 97% chance that it will be 22.” And also explic­itly list every per­son who has made an offer, what its price level is, and and how dif­fer­ent offers are in effect. What we want, hon­estly, is to pres­sure the vis­i­tor into buy­ing now or mak­ing a higher offer than any­body else’s. And trans­parency is the key to that.

Unlike a Yan­kee (eBay-​​style) auc­tion sale, low­ball offers are post­poned, not imme­di­ate. In a ratchet auc­tion, it seems that the incen­tive to bid is spread out more evenly in time, whereas a Yan­kee auc­tion increases pres­sure to bid towards the sched­uled end­point. By spread­ing out the pres­sure to bid, I’ll argue that a ratchet auc­tion caters to asyn­chro­nous vis­its by poten­tial cus­tomers, could as a result lead to improved sales prices in sit­u­a­tions where you do not have the full and syn­chro­nized atten­tion of the marketplace.

Like an online site, say.

Ron Jef­fries notes that what I’ve described now could be man­aged by hand by a seller, if the period was suf­fi­ciently long. You could, I sup­pose, just change the prices in your store­front and update the accom­pa­ny­ing graphs, and accept offers via email. There is a small mat­ter of get­ting the cus­tomers to trust that you’re not ratch­et­ing the price up in response to their offers — but you know, there always is, isn’t there? And there’s still a prob­lem in get­ting peo­ple to see your offer­ings in the first place.

Sounds like there are some things left unre­solved. I have some ideas, but I’m tired. I’ll get to them in a bit.

In the mean­time, con­sider how it is you came across this lit­tle entry of mine. There are so many other things for you to read. How is it that you’re here, now?