Learning Strategies in Decentralized Matching Markets under Uncertain Preferences
This work addresses the challenge of learning preferences in decentralized resource allocation, which is incremental as it builds on existing matching market frameworks with a focus on uncertainty and competition.
The paper tackles the problem of decision-making in decentralized matching markets where agents' preferences are unknown and must be learned from data, showing that their estimator converges at a minimax optimal rate and deriving optimal strategies with properties like stability and fairness.
We study the problem of decision-making in the setting of a scarcity of shared resources when the preferences of agents are unknown a priori and must be learned from data. Taking the two-sided matching market as a running example, we focus on the decentralized setting, where agents do not share their learned preferences with a central authority. Our approach is based on the representation of preferences in a reproducing kernel Hilbert space, and a learning algorithm for preferences that accounts for uncertainty due to the competition among the agents in the market. Under regularity conditions, we show that our estimator of preferences converges at a minimax optimal rate. Given this result, we derive optimal strategies that maximize agents' expected payoffs and we calibrate the uncertain state by taking opportunity costs into account. We also derive an incentive-compatibility property and show that the outcome from the learned strategies has a stability property. Finally, we prove a fairness property that asserts that there exists no justified envy according to the learned strategies.