Optimal Sale: Auctions with a Buy-Now Option
We characterize the optimal selling mechanism in a scenario where similar goods are sold to “high end” buyers through a posted price and to “lower end” buyers through an auction. We show that the optimal mechanism involves an auction which is a standard optimal auction (Myerson (1981)) up to a critical type. Types above the critical type are pooled. Further, the allocation probability jumps up at the critical type and is the maximal possible for the pooled types. Therefore other than pooling at the top, the optimal mechanism allocates the object as efficiently as in a standard optimal auction. We show that posted price selling followed by auctions with a “temporary” buy-now option implements the optimal mechanism. Auctions with such an option are in widespread use on eBay.
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