[3O4-GS-5] Agents: social-problem solving

[3O4-GS-5-05] Regulating Matching Markets with Constraints: Data-driven Taxation

Akira Matsushita¹, Kei Ikegami², Kyohei Okumura³, Yoji Tomita⁴, 〇Atsushi Iwasaki⁵ (1. University of Tokyo, 2. New York University, 3. Northwestern University, 4. Cyber Agent, Inc. , 5. University of Electro-Communications)

[[Online]]

Keywords:Matching with Constraints, Transferrable Utilities, Data-Driven Mechanism Design

Real-world matching markets often restrict the number of matches for a specific group or type of agents. In fact, in a medical residency match, a policymaker often needs to guarantee the number of doctors working in rural areas to achieve the minimum standards for health care. Toward the goal, this paper proposes a tax scheme to regulate matching outcomes so that the policymaker meets the upper and lower bound constraints on the number of matches. First, we describe a transferable utility matching model with unobserved heterogeneity in preferences; the model allows us to estimate the preferences of agents using observed data on matching, i.e., who is matched with whom.
Then, we prove that there is a unique social welfare maximizing tax scheme that satisfies the constraints. We also show that the tax scheme can be obtained by solving a convex programming problem.
Furthermore, we numerically evaluate our method in an artificial matching market with regional constraints.