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.)