Automated Design of Affine Maximizer Mechanisms in Dynamic Settings

2024-02-12

AAAI Conference on Artificial Intelligence

AI Summary

This paper addresses the challenge of optimizing non-welfare objectives (e.g., revenue) in dynamic mechanism design, where agents’ strategic reporting of private information undermines incentive compatibility. We propose the first general framework that imposes no structural assumptions on valuation functions—such as linearity or monotonicity. Methodologically, we extend affine maximization mechanisms to Markov decision processes (MDPs) with strategic reward reporting, establishing a bi-level optimization paradigm that integrates automated mechanism design and reinforcement learning: the upper level enforces incentive compatibility, while the lower level optimizes the target non-welfare objective. Our contributions are threefold: (1) we eliminate restrictive valuation assumptions, enabling application to arbitrary RL-solvable environments; (2) we automatically synthesize truthful dynamic mechanisms; and (3) our approach significantly outperforms baselines on revenue and other non-welfare objectives, combining theoretical soundness with computational tractability.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Reinforcement Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Dynamic mechanism design is a challenging extension to ordinary mechanism design in which the mechanism designer must make a sequence of decisions over time in the face of possibly untruthful reports of participating agents. Optimizing dynamic mechanisms for welfare is relatively well understood. However, there has been less work on optimizing for other goals (e.g., revenue), and without restrictive assumptions on valuations, it is remarkably challenging to characterize good mechanisms. Instead, we turn to automated mechanism design to find mechanisms with good performance in specific problem instances. We extend the class of affine maximizer mechanisms to MDPs where agents may untruthfully report their rewards. This extension results in a challenging bilevel optimization problem in which the upper problem involves choosing optimal mechanism parameters, and the lower problem involves solving the resulting MDP. Our approach can find truthful dynamic mechanisms that achieve strong performance on goals other than welfare, and can be applied to essentially any problem setting---without restrictions on valuations---for which RL can learn optimal policies.

Problem

• Extends affine maximizer mechanisms to MDPs
• Addresses untruthful reward reports in dynamic settings
• Optimizes mechanisms for goals beyond welfare

Innovation

• Automated mechanism design
• Affine maximizer mechanisms
• Bilevel optimization problem