Learning Optimal Dynamic Matching via Graph Neural Networks

Dynamic matching markets require decisions about whom to match and when: matching now yields value but removes participants who may create better future opportunities. We develop a value-based reinforcement-learning framework for this problem on finite, evolving weighted graphs. We study an infinite-horizon continuous-time model with stochastic arrivals, node-type transitions, edge realizations, and exogenous exits. We prove an event-time reduction: without loss of optimality, the planner acts immediately after each exogenous event and then waits for the next one. We further show that the optimal edge-wise $Q$-function is characterized by a single continuation-value function on post-decision residual graphs, reducing the learned object from state-action values to graph values. Exact action selection still requires combinatorial matching optimization; we approximate the value with a graph neural network, train it by temporal-difference learning, and use it in a forward-greedy matching heuristic. In a binary-type benchmark, the learned policy substantially outperforms immediate and threshold-greedy rules by preserving common nodes for rare arrivals of valuable matches while forming lower-value matches only in thick pools. In a kidney paired donation benchmark, it performs similarly to immediate greedy when exits are unpredictable, recovers the logic of patient matching when warnings are reliable, and outperforms the better of Immediate Greedy and Patient Greedy across intermediate warning probabilities. These results show that residual-graph value learning yields state-dependent dynamic matching policies that adapt to realized connectivity and exit information.

No Screening is More Efficient with Multiple Objects

We study efficient mechanism design for allocating multiple heterogeneous objects. We aim to maximize the residual surplus, the total value generated from an allocation minus the costs for screening agents' values. We discover a robust trend indicating that no-screening mechanisms such as serial dictatorship with exogenous priority order tend to perform better as the variety of goods increases. We analyze the underlying reasons by characterizing efficient mechanisms in a stylized environment. We also apply an automated mechanism design approach to numerically derive efficient mechanisms and validate the trend in general environments. Building on this implication, we propose the register-invite-book system (RIB) as an efficient system for scheduling vaccination against pandemic diseases.