An indivisible object may be sold to one of n agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the valuations' distribution is scarce: she knows only the means (which may be different) and an upper bound for valuations. Valuations may be correlated. Using a constructive approach based on duality, we prove that a mechanism that maximizes the worst-case expected revenue among all deterministic dominant-strategy incentive compatible, ex post individually rational mechanisms takes the following form: (1) the bidders submit bids b_i; (2) for each bidder, a linear score s_i=\beta_ib_i-\alpha_i is calculated where \alpha_i, \beta_i are fixed parameters; (3) the object is  awarded to the agent with the highest score, provided it 's nonnegative; (4) the winning bidder pays the minimal amount he would need to bid to still win in the auction . The set of optimal mechanisms includes other mechanisms but all those have to be close to the optimal linear score auction in a certain sense. When means are high, all optimal mechanisms share the linearity property. Second-price auction without a reserve is an optimal mechanism when the number of symmetric bidders is sufficiently high.
An indivisible object may be sold to one of n agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the valuations' distribution is scarce: she knows only the means (which may be different) and an upper bound for valuations. Valuations may be correlated. Using a constructive approach based on duality, we prove that a mechanism that maximizes the worst-case expected revenue among all deterministic dominant-strategy incentive compatible, ex post individually rational mechanisms is such that the object should be awarded to the agent with the highest linear score provided it is nonnegative. Linear scores are bidder-specific linear functions of bids . The set of optimal mechanisms includes other mechanisms but all those have to be close to the optimal linear score auction in a certain sense. When means are high, all optimal mechanisms share the linearity property. Second-price auction without a reserve is an optimal mechanism when the number of symmetric bidders is sufficiently high.
D
takes the following form: (1) the bidders submit bids b_i; (2) for each bidder, a linear score s_i=\beta_ib_i-\alpha_i is calculated where \alpha_i, \beta_i are fixed parameters; (3) the object
A
such that the object should be
R
score, provided it 's nonnegative; (4) the winning bidder pays the minimal amount he would need to bid to still win in the auction
linear score provided it is nonnegative. Linear scores are bidder-specific linear functions of bids