Can the auctioneer bid at an auction?

No, it would be inappropriate and is even illegal in many circumstances (called shill bidding). It is completely illegal in the state of Pennsylvania.
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As with the seller, the auctioneer is usually not allowed to bid (see below). In a "no reserve" auction, the seller and his agents are legally prohibited from bidding. The seller is almost always allowed to bid in a forced or seizure auction.
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Can the auctioneer bid?
The answer is yes, if:
1. The seller has knowledge and consent
2. The auctioneer wishes to bid
3. The buyers are informed of this right to bid
4. The governing law does not prohibit it

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However, this is restricted by law, or by auction groups themselves. Bidding by an auctioneer is allowed for proxy bidding and by the sellers when there is a reserve price set. The auctioneer is essentially "buying back" an item, but most states require this to be announced before any bidding takes place.
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Most bidding excludes the auctioneer to eliminate any appearance of impropriety and to avoid discouraging other bidders. On auction sites like Ebay it is physically impossible for a seller to bid on the item they are selling, even if selling it for another party (this is to prevent shill bidding).

Proxy Bidding
Small auction houses may allow for proxy bidding by the auctioneer. He will announce it when the Lot or Item is brought up to the podium and described. If it's challenged, he must be able to show documentation and verification of the proxy bid to the satisfaction of the opposing bidders, or the state regulatory agency if required to do so by that body. This is done for absentee bidders that cannot do phone bids at the time of the auction. These bids must be placed at the viewing date or by phone prior to the Auction. The auctioneer, staff , or immediate family may not bid up for proxy bidders.