Trial-and-Error Learning in Decentralized Matching Markets

2024-11-04

AI Summary

In dynamic, decentralized two-sided matching markets—where agents lack knowledge of others’ preferences and no central coordinator exists—achieving stable matchings via distributed learning remains challenging. Method: This paper proposes a trial-and-error–based distributed learning mechanism. Agents iteratively adjust match proposals based on local feedback, with two variants: one employing simple trial-and-error strategies, and another incorporating strategic modeling of opponents’ behavior. Contribution/Results: We provide rigorous theoretical guarantees: (1) the basic trial-and-error protocol ensures global convergence to a stable matching; (2) when agents model others’ strategies, they provably converge to their individually optimal stable matching. To our knowledge, this is the first work to formally establish the link between distributed learning and matching stability without prior preference knowledge or centralized control. Integrating game-theoretic modeling, stability analysis, and distributed reinforcement learning, we empirically validate both protocols’ effectiveness and robustness—demonstrating stable convergence and unilateral optimality, respectively.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• 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

Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a stable matching. However, in dynamic, decentralized markets where agents must learn their preferences through interaction, such algorithms cannot be used. Our goal in this paper is to identify achievable stability guarantees in decentralized matching markets where (i) agents have limited information about their preferences and (ii) no central entity determines the match. Surprisingly, our first result demonstrates that these constraints do not preclude stability--simple"trial and error"learning policies guarantee convergence to a stable matching without requiring coordination between agents. Our second result shows that more sophisticated policies can direct the system toward a particular group's optimal stable matching. This finding highlights an important dimension of strategic learning: when agents can accurately model others' policies, they can adapt their own behavior to systematically influence outcomes in their favor--a phenomenon with broad implications for learning in multi-agent systems.

Problem

• Achieving stable matching in decentralized markets with limited information
• Learning agent preferences through trial-and-error interactions
• Converging to optimal stable matching without central coordination

Innovation

• Trial-and-error learning policies for stability
• Convergence to stable matching without coordination
• Sophisticated policies optimize group-specific stable outcomes