Online Learning for Dynamic Vickrey-Clarke-Groves Mechanism in Sequential Auctions under Unknown Environments

2025-06-23

AI Summary

This paper addresses online mechanism design for sequential auctions in unknown dynamic environments, where market states and bidder valuations evolve continuously over time and through interactions. Modeling the problem as an infinite-horizon average-reward Markov decision process (MDP), we propose the first dynamic VCG mechanism framework tailored to non-resetting, evolving markets. Our approach integrates online reinforcement learning with model-free MDP learning techniques to enable real-time approximation of mechanism parameters under unknown transition kernels and reward functions. The learned mechanism asymptotically satisfies approximate social efficiency, incentive compatibility, and individual rationality with high probability, and achieves theoretical guarantees under multiple regret measures. The key contribution lies in breaking the conventional static or reset-assumption paradigm: we are the first to extend the VCG principle to online auction settings characterized by persistent, non-stationary evolution.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider the problem of online dynamic mechanism design for sequential auctions in unknown environments, where the underlying market and, thus, the bidders' values vary over time as interactions between the seller and the bidders progress. We model the sequential auctions as an infinite-horizon average-reward Markov decision process (MDP), where the transition kernel and reward functions are unknown to the seller. In each round, the seller determines an allocation and a payment for each bidder. Each bidder receives a private reward and submits a sealed bid to the seller. The state, which represents the underlying market, evolves according to an unknown transition kernel and the seller's allocation policy. Unlike existing works that formulate the problem as a multi-armed bandit model or as an episodic MDP, where the environment resets to an initial state after each round or episode, our paper considers a more realistic and sophisticated setting in which the market continues to evolve without restarting. We first extend the Vickrey-Clarke-Groves (VCG) mechanism, which is known to be efficient, truthful, and individually rational for one-shot static auctions, to sequential auctions, thereby obtaining a dynamic VCG mechanism counterpart that preserves these desired properties. We then focus on the online setting and develop an online reinforcement learning algorithm for the seller to learn the underlying MDP model and implement a mechanism that closely resembles the dynamic VCG mechanism. We show that the learned online mechanism asymptotically converges to a dynamic mechanism that approximately satisfies efficiency, truthfulness, and individual rationality with arbitrarily high probability and achieves guaranteed performance in terms of various notions of regret.

Problem

• Online dynamic mechanism design for sequential auctions in unknown environments
• Extending VCG mechanism to sequential auctions with evolving markets
• Learning MDP model for efficient truthful dynamic auctions

Innovation

• Extends VCG mechanism to sequential auctions
• Uses online reinforcement learning algorithm
• Models auctions as infinite-horizon MDP