Optimal Incentive Design for Decentralized Dynamic Matching Markets

Abstract

In decentralized dynamic matching markets, agents can benefit from sharing resources, but they will collaborate only if properly incentivized. Motivated by applications such as multi-hospital kidney exchanges and job-hunting markets, this paper proposes novel monetary and non-monetary mechanisms to incentivize collaboration in such decentralized dynamic markets. We study a model in which multiple self-interested agents manage local multi-way dynamic matching problems. Jobs of different types arrive stochastically at each agent, expire after a limited time, and yield rewards when matched. An agent’s job backlog and actions are her private information, and each agent aims to maximize her long-run average matching reward.

We design simple mechanisms that incentivize agents to submit all jobs upon arrival, thereby enabling centralized matching. Our first mechanism, the Marginal-Value (MV) mechanism, reimburses agents based on the marginal value of their submitted jobs. This can also be implemented in a non-monetary way by randomly selecting an agent (with a specified probability) to perform a match and collect the associated matching reward. We show that under the MV mechanism, full job submission constitutes an approximate Nash equilibrium—that is, the gain from unilateral deviation vanishes as the number of agents grows. To further eliminate incentives for deviation, we propose a refined mechanism, the Marginal-Value-plus-Credit (MVC) mechanism, and show that when the number of agents exceeds a constant threshold, full job submission constitutes a stronger oblivious equilibrium. Numerical experiments based on kidney exchange data demonstrate that the gains from deviation under our mechanisms are small even in moderately sized markets.

Keywords: Decentralized matching, incentive design, market design, dynamic matching, dynamic games