Dynamic Matching in Overloaded Waiting Lists

Leshno, Jacob D.

doi:10.2139/ssrn.2967011

Cited by 51 publications

(59 citation statements)

References 25 publications

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“…7 A patient-donor pair cannot be matched in any matching if it cannot form a (two-way) exchange with any other patient-donor pair due to biological compatibility. 15 See also related results in queueing models (Leshno, 2014;Bloch and Cantala, 2016). 16 The paper restricts attention to matching only pairs of agents and not through chains.…”

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confidence: 95%

Matching in Dynamic Imbalanced Markets

2018

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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 ...

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confidence: 95%

Matching in Dynamic Imbalanced Markets

2018

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“…A complementary class dynamic matching model examine one‐time matchings that arise over multiple periods. Here, focus has ranged from questions of preference formation (Kadam, ) and unraveling (Roth and Xing, ) to managing the (stochastic) arrival and departure of agents or objects (Ünver, ; Baccara et al., ; Thakral, ; Akbarpour et al., ; Leshno, ). Doval () examines an economy of this latter type and independently proposes a definition of “dynamic stability,” which is distinct from our proposal.…”

Section: Literaturementioning

confidence: 99%

Multiperiod Matching

Kadam

Kotowski

2018

Int Economic Review

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We examine a dynamic, two‐sided, one‐to‐one matching market where agents on both sides interact over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments. A generalization of the deferred acceptance algorithm can identify dynamically stable outcomes in a large class of economies, including cases with intertemporal preference complementarities. We relate our analysis to market unraveling and to common market design applications, including the medical residency match.

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“…While the design of such systems has garnered significant research attention, most theoretical results yield answers that depend on the primitives of the market (compare Su and Zenios 2004;Leshno 2017;Bloch and Cantala 2017). Moreover, the state of the art empirical methods used to prospectively evaluate wait list designs do not incorporate the dynamic incentives that are central to the theoretical literature.…”

Section: Dynamic Incentives In Wait List Mechanisms †mentioning

confidence: 99%

“…Indeed, Bloch and Cantala (2017) show that FCFS yields better match value than any mechanism that gives agents that have waited longer weakly higher priority. However, this result depends on the nature of primitives as shown in Leshno (2017), who studies a model with agents that have preferences for a specific type of object. He shows that it may be optimal to run a lottery among agents at the "top positions" to influence selectivity and reduce misallocation.…”

Section: A Numerical Examplementioning

confidence: 99%

Dynamic Incentives in Wait List Mechanisms

Agarwal

Ashlagi

Somaini

et al. 2018

AEA Papers and Proceedings

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Many scarce public resources are allocated through wait lists that use priorities for individual agents. A new priority system for allocating deceased donor kidneys was adopted in 2014. This redesign was guided by simulations that held decision-rules fixed. We synthesize recent theoretical results to show that the welfare effects of a mechanism depend on the interaction between dynamic incentives and heterogeneity in preferences. We show evidence suggesting that patient decisions on the deceased donor kidney wait list respond to dynamic incentives. Therefore, an empirical approach to dynamic mechanism design is an essential complement to mechanism design theory in dynamic environments.

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Dynamic Matching in Overloaded Waiting Lists

Cited by 51 publications

References 25 publications

Matching in Dynamic Imbalanced Markets

Matching in Dynamic Imbalanced Markets

Multiperiod Matching

Dynamic Incentives in Wait List Mechanisms

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