An auctioneer is never tempted to employ a shill bidder.
To be sure, he might want to make the winning bidder pay a higher price and using a shill bidder is one way to make that happen. For example, in an English auction the seller could shill bid until the price reaches a point where all but one bidders have dropped out. That price is the highest revenue he would have earned without shill bidding, and by shilling a little bit longer before finally dropping out, the seller could try to extract something more.
Of course, this comes at some risk for the seller because there is a chance that the high bidder will drop out before the shill bidder does and then the seller misses out on a sale. Nevertheless, a shill bidder pays off on average if the seller thinks that this small-probability loss is outweighed by the large-probability gain.
Nevertheless, the seller would never be tempted to do this.
The reason is that he could achieve exactly the same thing using reserve price. Before the auction even begins he can ask himself what he would want to do if the price rose to that level. If he decided that he would want to use a shill bidder to raise the price even further then he could bring about exactly the same effect by setting his reserve price at the desired level.
That is, a shill bidder is just a reserve price in disguise.
(ps, you don’t have to get very fancy to see why this is wrong.)
Cheap Talk 
6 comments
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October 25, 2011 at 11:25 pm
ryan
can’t you choose to accept a winning bid if it’s just below the share price, by, say, a penny, while with a shill bidder, you’d lose the chance to take that price, instead gambling that they’d bid again above your reserve?
October 25, 2011 at 11:25 pm
ryan
reserve price, not share price.
October 26, 2011 at 12:42 am
Kevin
you learn about the distribution of valuations during the auction. The shill bidder lets you condition your reservation wage on this information.
October 26, 2011 at 12:50 am
Evan
+1 for Kevin.
The interesting question for me is: Why did Jeff decide to share this with us? Is it a benevolent gesture simply intended to amuse us? Is it an encouragement to young aspiring theorists that sometimes even good theorists are wrong?
October 26, 2011 at 9:03 am
Michael
In addition to what Kevin said, by creating fake demand, you hope to cause other bidders to overvalue the object you are selling.
October 27, 2011 at 9:17 am
jeff
Various counter-arguments:
1. correlation. Suppose there are three bidders and values are correlated. Then the point at which the first bidder drops out of the auction gives you information about the others values. Now when there is just one bidder left you want to use that information to set the reserve price of the remaining bidder. With a fixed reserve price you don’t have that flexibility. A shill bidder gives you that. Note that this argument requires at least 3 bidders.
2. asymmetry. when values are distributed asymmetrically you want a different reserve price for different bidders. A shill bidder allows you to condition the reserve price on who is the final remaining bidder.
But the simplest refutation works even if there are only two bidders, they are symmetric and values are independent. If the price rises to p and the second to last bidder drops out, i may want to raise the price paid by the last bidder. i can do that with a shill bidder. if i do it with a reserve price then i also am committing not to sell at any price below p. I may not want to do that.
For example, there are cases where the second-to-last bidder drops out at a price q<p and at that stage i don't want to raise the price any further. (the trade-off discussed in my post is unfavorable). A fixed reserve price forces me to choose one or the other, i.e. if i sell at q i must sell at p. if i don't sell at p, i can't sell at q either.
I can instruct my shill bidder to stay out until the price rises to p and only then start bidding. This makes my reserve price flexible.
For auction theory insiders, that flexibility is useful when Myerson's regular case fails. On the other hand when the monotone hazard rate condition is satisfied, i never value that flexibility and the equivalence of shill bidding and fixed reserve prices.