We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety may become available to the seller at each time and a random number of consumers may enter the market at each time. Each consumer is present in the market for one time step and wants to consume one good of one of its desired varieties. Each consumer is associated with a flexibility level that indicates the varieties of the goods it is equally interested in. A consumer's flexibility level and the utility it gets from consuming a good of its desired varieties are its private information. We characterize the allocation rule for a Bayesian incentive compatible, individually rational and expected revenue maximizing mechanism in terms of the solution to a dynamic program. The corresponding payment function is also specified in terms of the optimal allocation function. We leverage the structure of the consumers' flexibility model to simplify the dynamic program and provide an alternative description of the optimal mechanism in terms of thresholds computed by the dynamic program.

中文翻译：

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具有随机供给和灵活消费者的最优动态机制设计

我们考虑设计一个预期收入最大化机制的问题，用于在 $T$ 时间步长内将多个 $k$ 品种的不易腐烂的商品分配给灵活的消费者。在我们的模型中，每个品种的随机数量的商品每次都可能提供给卖家，并且每次都有随机数量的消费者进入市场。每个消费者都在市场上出现一个时间步长，并希望消费其所需品种中的一种。每个消费者都与一个灵活性水平相关联，该灵活性水平表明它同样感兴趣的商品种类。消费者的灵活性水平和从消费其所需种类的商品中获得的效用是其私人信息。我们描述了贝叶斯激励兼容的分配规则，就动态计划的解决方案而言，个人合理和预期的收入最大化机制。相应的支付函数也根据最优分配函数来指定。我们利用消费者灵活性模型的结构来简化动态程序，并根据动态程序计算的阈值提供最佳机制的替代描述。