Automated Many-to-One Matching Mechanism Design Using Deep Learning

Shota Kimata, Yuko Sakurai

Abstract: In this paper, we consider the design of a many-to-one matching mechanism using deep learning. Traditionally, matching theory has been studied in the fields of game theory and microeconomics. Artificial intelligence (AI) researchers have proposed various types of practical matching mechanism, such as kidney exchange. In general, the design of matching mechanisms has been carried out manually. However, with recent advances in deep learning, a learning framework for matching mechanisms using deep learning has been proposed. This matching framework using deep learning focuses on one-to-one matching and involves the learning of matching mechanisms that consider the trade-off between stability and strategy-proofness. On the other hand, in the real world, there exist a lot of many-to-one matching problems, such as school choice. Therefore, in this paper, we extend the matching framework using deep learning to handle many-to-one matching. Furthermore, since existing research has not considered social welfare, we formulate the many-to-one matching problem as an optimization problem that maximizes the expected social welfare under the constraints of strategy-proofness and stability. In computational experiments, we analyze the trade-off between stability and strategy-proofness. We show that the mechanism learned using a neural network can balance the trade-off between stability and strategy-proofness. Furthermore, we show that expected social welfare exceeds the RSD mechanism in most cases.