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A single seller faces a sequence of buyers with unit demand. The buyers are forward‐looking and long‐lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive‐compatible mechanism has to induce truth‐telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth‐telling constraint regarding the arrival time can be represented as an optimal stopping problem that determines the first time at which the buyer participates in the mechanism. The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time.more » « less
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Bergemann, Dirk ; Heumann, Tibor ; Morris, Stephen ( , The RAND Journal of Economics)null (Ed.)
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Bergemann, Dirk ; Brooks, Benjamin ; Morris, Stephen ( , Theoretical Economics)null (Ed.)We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of the bidders' independent signals. If the revenue maximizing solution is to sell the object with probability 1, 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 1, then optimal mechanisms skew the allocation toward 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.more » « less