Working Paper: CEPR ID: DP13332
Authors: Dirk Bergemann; Benjamin A. Brooks; Stephen Morris
Abstract: We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of bidders’ independent signals. If the revenue maximizing solution is to sell the object with probability one, then an optimal mechanism is simply a posted price, namely, the highest price such that every type of every bidder is willing to buy the object. If the object is optimally sold with probability less than one, then optimal mechanisms skew the allocation towards bidders with lower signals. The resulting allocation induces a “winner’s blessing,” whereby the expected value conditional on winning is higher than the unconditional expectation. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the first-price, second-price or English auctions) deliver lower revenue because of the winner’s curse generated by the allocation. Our qualitative results extend to more general common value environments with a strong winner’s curse.
Keywords: optimal auction; common values; maximum; game; posted price; revenue equivalence; adverse selection; neutral selection; advantageous selection
JEL Codes: C72; D44; D82; D83
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| standard auctions (first-price, second-price, English) (D44) | lower revenue (H27) |
| inclusive posted price mechanism (D49) | higher revenue (H27) |
| random twotier posted price mechanism (D49) | higher revenue (H27) |
| random twotier posted price mechanism (D49) | skewing allocation towards lower-signal bidders (D44) |
| skewing allocation towards lower-signal bidders (D44) | winners blessing (D44) |
| winners curse (D44) | bid shading (D44) |
| winners curse (D44) | expected value conditional on winning < unconditional expectation (D81) |
| random twotier posted price maximizes revenue (D40) | reversing winners curse into winners blessing (D44) |