Optimal Auction Design for Dynamic Stochastic Environments: Myerson Meets Naor

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Abstract: Allocation of goods and services often involves both stochastic supply and stochastic demand. Motivated by applications such as cloud computing, gig platforms, and blockchain auctions, we study the design of optimal selling mechanisms in an environment where buyers with private valuations arrive stochastically and are assigned goods that also arrive stochastically, and either buyers or goods can be held in a queue at costs until allocation. We derive the dynamic screening mechanism that optimally manages the inventory of goods, the customer queue, and the competition between customers, through reserve prices that increase with queue length and an auction to allocate the goods.