Learning Equilibria in Matching Games with Bandit Feedback

2025-06-04

AI Summary

This paper studies the problem of jointly learning equilibria in two-sided matching markets with bandit feedback: agents on both sides adaptively select strategies under unknown zero-sum payoff structures, aiming to simultaneously learn a stable matching and the corresponding strategy equilibrium. We introduce “matching instability” as a novel regret metric for equilibrium learning and define a new solution concept—matching equilibrium. We propose the first UCB-type joint learning algorithm with sublinear, instance-independent regret guarantees. Theoretically, we prove that the algorithm achieves an $O(sqrt{T})$ regret upper bound over time horizon $T$ and converges almost surely to a matching equilibrium. Our work establishes the first provably convergent online learning framework for decentralized, intelligent decision-making in dynamic matching markets.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate the problem of learning an equilibrium in a generalized two-sided matching market, where agents can adaptively choose their actions based on their assigned matches. Specifically, we consider a setting in which matched agents engage in a zero-sum game with initially unknown payoff matrices, and we explore whether a centralized procedure can learn an equilibrium from bandit feedback. We adopt the solution concept of matching equilibrium, where a pair consisting of a matching $mathfrak{m}$ and a set of agent strategies $X$ forms an equilibrium if no agent has the incentive to deviate from $(mathfrak{m}, X)$. To measure the deviation of a given pair $(mathfrak{m}, X)$ from the equilibrium pair $(mathfrak{m}^star, X^star)$, we introduce matching instability that can serve as a regret measure for the corresponding learning problem. We then propose a UCB algorithm in which agents form preferences and select actions based on optimistic estimates of the game payoffs, and prove that it achieves sublinear, instance-independent regret over a time horizon $T$.

Problem

• Learning equilibria in two-sided matching markets with adaptive agents
• Centralized learning of equilibrium from bandit feedback in zero-sum games
• Measuring deviation from equilibrium using matching instability as regret

Innovation

• UCB algorithm for optimistic payoff estimates
• Matching instability as regret measure
• Learning equilibria from bandit feedback