Matching in Dynamic Imbalanced Markets

Abstract

We study dynamic matching in exchange markets with easy-and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents generate by facilitating future matchings. We prove that this trade-off between a "thicker" market and faster matching vanishes in large markets; A greedy policy leads to shorter waiting times, and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly-used policies (1.6% more than monthly-batching), and shorter patient waiting times (23 days faster than monthly-batching). moved from matching roughly every month to matching daily. 3 Practitioners are concerned that this behavior, some of which is driven by competition between Kidney exchanges, 4 is harmful, especially for the most highly sensitized patients. 5 In contrast, kidney exchange programs in Canada, Australia, and the Netherlands match periodically every 3 or 4 months (Ferrari et al., 2014).This article analyses the trade-off between agents' waiting times and the percentage of matched agents in dynamic markets. We find that, maybe surprisingly, matching greedily minimizes the waiting time and simultaneously maximizes the chances to find a compatible partner for all agents for sufficiently large markets. We further quantify the inefficiency associated with other commonly used policies like monthly matching using data from the National Kidney Registry.To analyze this question we propose a stochastic compatibility model with easy-to-match and hard-to-match agents. Easy-to-match agents can match with all other agents with a positive probability p, whereas hard-to-match agents can match only with easy-to-match agents with a positive probability q. The main focus of our analysis is on the case where the majority of agents are hard-to-match, which is inline with kidney exchange pools. This model captures two empirical regularities of the patient-donor data from the National Kidney Registry (NKR): First, as the market grows large, the fraction of patient-donor pairs that are matched in a maximal matching does not approach 1, which is a consequence of the imbalance between different pairs' blood types in kidney exchange (Saidman et al., 2006;Roth et al., 2007). 6 Second, as the market grows large, the fraction of agents that cannot be matched in any matching goes to zero. 7 Our parsimonious two-type model captures the above regularities and no single-type model can account for both of them (Propositions 1 and 2).We study a dynamic model based on the above two-type compatibility structure in which easyand hard-to-match agents arrive to the market according to independent Poisson processes with rates m E and m H . Agents depart exogenously at rate d. The market-maker observes the realized compatibilities and decides when to match compatible agents. We evaluate a policy based on three measures: match rate, matching time, and waiting time. The match ...

Asymptotically Optimal Control of a Centralized Dynamic Matching Market with General Utilities

“…In a static matching market, even a slight imbalance can give rise to a unique stable matching (Ashlagi et al 2017a). We also note that a greedy policy is optimal in a somewhat different unbalanced market setting, where easy-to-match agents can match with all other agents in the market with a specified probability, but hard-to-match agents can match only with easy-to-match agents with a different specified probability (Ashlagi et al 2018a). In our analysis of the utility threshold policy in the heavy-tailed case of an unbalanced market, we obtain the somewhat surprising result that the solution is symmetric; that is, the utility threshold is the same for buyers and sellers.…”

Kidney Exchange: An Operations Perspective

“…42 One stream of papers considers models in which compatibilities are based on random graphs, modeling the sparsity due to sensitivity of patients. Several of these papers assume that nodes (pairs) do not depart the pool unless matched (Anderson et al 2017;Ashlagi et al 2018aAshlagi et al , 2019aBlum and Mansour 2020). These papers find that greedy matching is optimal Ashlagi and Roth: Kidney Exchange: An Operations Perspective when minimizing average waiting times.…”

“…43 Other papers assume that nodes depart the pool according to some hazard rate. Akbarpour et al (2020b) seeks to maximize the number of matches, and Ashlagi et al (2018a) analyzes the trade-offs between waiting times and the number of matches. These papers also find greedy matching to be optimal in a large market.…”

A Time Bank System Design on the Basis of Hyperledger Fabric Blockchain

“…(3) Service Matching: After the service proposals are posted on SC, the proposed system tries to find matches as much as possible. Without a loss of the generality, this paper just uses a simple (intuitive) matching scheme to find matches while there are other complicated matching algorithms [13][14][15], whose adoption would enhance the matching performance. Either SP or SR needs to take all the attributes (except the location-related one) into comparison so as to find the matched services.…”