  In a single-item auction, a duplicitous seller may masquerade as one or more
bidders in order to manipulate the clearing price. This paper characterizes
auction formats that are shill-proof: a profit-maximizing seller has no
incentive to submit any shill bids. We distinguish between strong
shill-proofness, in which a seller with full knowledge of bidders' valuations
can never profit from shilling, and weak shill-proofness, which requires only
that the expected equilibrium profit from shilling is nonpositive. The Dutch
auction (with suitable reserve) is the unique optimal and strongly shill-proof
auction. Moreover, the Dutch auction (with no reserve) is the unique
prior-independent auction that is both efficient and weakly shill-proof. While
there are a multiplicity of strategy-proof, weakly shill-proof, and optimal
auctions; any optimal auction can satisfy only two properties in the set
{static, strategy-proof, weakly shill-proof}.
