Optimal Auction Design for Dynamic Stochastic Environments: Myerson Meets Naor

2025-05-28

AI Summary

We study dynamic auctions where both buyer valuations and item supplies arrive stochastically over time, and buyers may queue at a cost. Method: We propose the first online sequential auction framework integrating Myerson’s optimal auction theory with Naor’s queueing theory. We design state-dependent, time-varying reserve prices—increasing in queue length and decreasing in inventory—to explicitly capture intertemporal competition and waiting costs. Using an interdisciplinary model combining mechanism design, stochastic control, and dynamic programming, we derive a Bayes-optimal revenue policy under general stochastic arrival processes, while rigorously ensuring incentive compatibility and individual rationality. Contribution/Results: Numerical experiments demonstrate 18%–32% revenue improvement over benchmark mechanisms. Our framework yields a deployable theoretical solution for real-world applications including cloud service pricing, gig-platform allocation, and blockchain-based auctions.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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. The optimal mechanism dynamically leverages competitive pressure across time by managing the queue of buyers and inventory of goods, using reserve prices that increase with the number of buyers in the queue and decrease with the number of items in inventory, and an auction to allocate the goods.

Problem

• Design optimal auctions for stochastic supply and demand environments
• Manage dynamic queues of buyers and inventory of goods
• Optimize reserve prices based on queue and inventory levels

Innovation

• Dynamic queue management for buyers
• Inventory-based adaptive reserve pricing
• Stochastic arrival auction allocation