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We study a Markov matching market involving a planner and a set of strategicagents on the two sides of the market. At each step, the agents are presentedwith a dynamical context, where the contexts determine the utilities. Theplanner controls the transition of the contexts to maximize the cumulativesocial welfare, while the agents aim to find a myopic stable matching at eachstep. Such a setting captures a range of applications including ridesharingplatforms. We formalize the problem by proposing a reinforcement learningframework that integrates optimistic value iteration with maximum weightmatching. The proposed algorithm addresses the coupled challenges of sequentialexploration, matching stability, and function approximation. We prove that thealgorithm achieves sublinear regret.

Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets