From Best Responses to Learning: Investment Efficiency in Dynamic Environment

2025-11-02

AI Summary

This paper addresses welfare guarantees in mechanism design under dynamic investment environments, where investors cannot instantaneously respond optimally due to incomplete information. We propose an adaptive decision-making framework via online learning algorithms to sustain near-optimal welfare over time. Methodologically, we integrate mechanism design with no-regret online learning, formulating a repeated interaction model and employing approximation ratio as the primary performance metric. Our theoretical contributions are threefold: (i) we prove that the welfare approximation ratio achieved in static settings remains unchanged under dynamic learning when benchmarked against ex-post optimal outcomes; (ii) for the more challenging time-varying benchmark, we establish the first tight upper and lower bounds on the approximation ratio; and (iii) we demonstrate that the proposed mechanism exhibits strong robustness to both uncertainty and learning delays. These results provide a novel paradigm for designing dynamic market mechanisms grounded in learning-augmented incentive compatibility and welfare efficiency.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: 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 study the welfare of a mechanism in a dynamic environment where a learning investor can make a costly investment to change her value. In many real-world problems, the common assumption that the investor always makes the best responses, i.e., choosing her utility-maximizing investment option, is unrealistic due to incomplete information in a dynamically evolving environment. To address this, we consider an investor who uses a no-regret online learning algorithm to adaptively select investments through repeated interactions with the environment. We analyze how the welfare guarantees of approximation allocation algorithms extend from static to dynamic settings when the investor learns rather than best-responds, by studying the approximation ratio for optimal welfare as a measurement of an algorithm's performance against different benchmarks in the dynamic learning environment. First, we show that the approximation ratio in the static environment remains unchanged in the dynamic environment against the best-in-hindsight benchmark. Second, we provide tight characterizations of the approximation upper and lower bounds relative to a stronger time-varying benchmark. Bridging mechanism design with online learning theory, our work shows how robust welfare guarantees can be maintained even when an agent cannot make best responses but learns their investment strategies in complex, uncertain environments.

Problem

• Analyzing welfare guarantees in dynamic investment environments
• Studying approximation ratios when investors learn adaptively
• Bridging mechanism design with online learning theory

Innovation

• Uses no-regret online learning algorithm
• Analyzes welfare guarantees in dynamic settings
• Bridges mechanism design with learning theory