We consider the problem of a seller who faces an unknown number of offers where each offer is a random draw from a known distribution. The objective of the seller is to maximize the probability that the highest offer is chosen. We show that the optimal strategy is characterized by a nonincreasing stochastic set of reservation prices. We also provide numerical analysis to calibrate the model and provide support to the observation that first offers in residential real estate markets tend to be higher than subsequent offers. The model's prediction closely matches the empirical findings of Merlo and Ortalo‐Magné that more than 70% of the properties sell to the buyer who makes the first offer.

中文翻译：

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接受或不接受：房地产销售商的最佳策略

我们考虑一个卖方面对未知数量的报价的问题，其中每个报价都是从已知分配中随机抽取的。卖方的目的是最大程度地选择最高出价。我们表明，最优策略的特征在于预订价格的随机增加。我们还提供数值分析以校准模型，并为以下观察结果提供支持：住宅房地产市场中的首次报价往往高于后续报价。该模型的预测与Merlo和Ortalo-Magné的经验发现非常吻合，即超过70％的房地产出售给提出第一个要约的买方。