Kidney exchange: An egalitarian mechanism

doi:10.1016/j.jet.2010.10.018

Journal of Economic Theory

Volume 146, Issue 2, March 2011, Pages 592-618

https://doi.org/10.1016/j.jet.2010.10.018 Get rights and content

Abstract

Kidney exchange programs utilize both deceased-donor and live-donor kidneys. One of these programs, a two-way kidney paired donation (KPD), involves two patients exchanging their live donorsʼ kidneys. Another possibility is a list exchange (LE): a living incompatible donor provides a kidney to a candidate on the deceased-donor waitlist and in return the intended recipient of this donor receives a priority on the waitlist. By taking into consideration the fact that transplants from live donors have a higher chance of success than those from cadavers, we characterize the set of efficient and egalitarian exchanges involving the KPDʼs and LEʼs.

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Cited by (23)

Efficient Kidney Exchange with Dichotomous Preferences
2021, Journal of Health Economics
Citation Excerpt :
Unver (2010) studied efficient kidney exchanges in a dynamic environment in which agents arrive according to a stochastic Poisson process. Yılmaz (2011) characterized an efficient and egalitarian two-way exchange mechanism involving paired donations and list exchanges. Nicoló and Rodríguez-Álvarez (2012) presented a model with match quality and patients’ preferences.
This paper studies a general kidney exchange model with compatible patient-donor pairs, incompatible patient-donor pairs, single donors, and patients on the waiting list. We derive an explicit formula of the maximal number of feasible kidney transplants under several sizes of cycles and chains of exchange, analyze the effect of different ways of exchange on efficiency, and provide substantial simulation results based on the USA data. Our results further show that kidney exchange can be decentralized for relatively large populations, and that allowing compatible pairs and single donors to exchange with incompatible pairs can significantly increase the number of feasible kidney transplants. A more general model of two-category type-compatible exchanges is also established.
Short trading cycles: Paired kidney exchange with strict ordinal preferences
2020, Mathematical Social Sciences
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They assume three-tiered preferences corresponding to the degree of compatibility. For another paper studying how randomization can improve equity in kidney exchanges under dichotomous preferences, see Yılmaz (2011). The mechanism I propose here is based on the Probabilistic Serial mechanism, initially defined by Bogomolnaia and Moulin (2001) in the simple object-assignment setting.
I study kidney exchange with strict ordinal preferences and with constraints on the lengths of the exchange cycles. Efficient deterministic mechanisms have poor fairness properties in this environment. Instead, I propose an individually rational, ordinally efficient and anonymous random mechanism for two-way kidney exchange based on Bogomolnaia and Moulin’s (2001) Probabilistic Serial mechanism. Individual rationality incentivizes patient–donor pairs who are compatible with each other to participate in the exchange, thus increasing the overall transplantation rate. Finally, individual rationality, ex-post efficiency and weak strategyproofness are incompatible for any mechanism.
Multi-unit assignment under dichotomous preferences
2020, Mathematical Social Sciences
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An intuitive solution equalizes agents’ utilities as much as possible respecting efficiency and individual rationality: this is the well-known leximin solution. I refer to it as the Egalitarian Solution (ES), proposed theoretically by BM04, and applied to kidney exchange by Roth et al. (2005) and Yılmaz (2011). The ES solution is well-defined and Lorenz dominant in the set of efficient utility profiles.
I study the problem of allocating objects among agents without using money. Agents can receive several objects and have dichotomous preferences, meaning that they either consider objects to be acceptable or not. In this set-up, the egalitarian solution is more appealing than the competitive equilibrium with equal incomes because it is Lorenz dominant, unique in utilities, and group strategy-proof. Both solutions are disjoint.
A one-sided many-to-many matching problem
2017, Journal of Mathematical Economics
This study discusses a one-sided many-to-many matching model wherein agents may not be divided into two disjoint sets. Moreover, each agent is allowed to have multiple partnerships in our model. We restrict our attention to the case where the preference of each agent is single-peaked over: (i) the total number of partnerships with all other agents, and (ii) the number of partnerships that the agent has with each of the other agents. We represent a matching as a multigraph, and characterize a matching that is stable and constrained efficient. Finally, we show that any direct mechanism for selecting a stable and constrained efficient matching is not strategy-proof.
Age-based preferences in paired kidney exchange
2017, Games and Economic Behavior
Citation Excerpt :
In recent years, PKE has received a considerable interest from both a theoretical and a practical design point of view. Most works have considered the framework that incorporates specific features consistent with the medical approach to PKE in New England (Roth et al., 2005a, 2005b, 2007; Hatfield, 2005; Ünver, 2010; Yılmaz, 2011, 2014). That approach assumes that only incompatible pairs participate in PKE, and that patients are indifferent between two compatible kidneys.
We consider a Paired Kidney Exchange (PKE) model in which patients' preferences are restricted so that patients prefer kidneys from compatible younger donors to kidneys from older ones. We propose a family of rules, sequential priority rules, that only allow for pairwise exchanges and satisfy individual rationality, efficiency, strategy-proofness, and non-bossiness. These rules allocate kidneys according to a priority algorithm that gives priority to patients with younger donors and assign kidneys from younger donors first. We extend the analysis to rules that allow multiple ways exchanges and to the case of patients who have more than one potential donor.
On the operation of multiple matching markets
2016, Games and Economic Behavior
We provide a new perspective on how to operate matching markets when there are many types of markets. Our finding is that the market-wise adaptation of strategy-proof and non-wasteful rules yields a strategy-proof rule with the following efficiency property: no strategy-proof rule Pareto-dominates the rule. Such rules are abundant as they include the market-wise use of the well-known priority-based rules of the top trading cycles and the deferred acceptance. This result gives theoretical support to the independent operation of markets observed in real-life markets as well as our practice in Market Design that separately treats each market for its design.

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¹: I would like to thank Tayfun Sönmez and Utku Ünver for helpful comments and conversations. I also would like to thank an associate editor of the journal as well as two anonymous referees for useful suggestions. I gratefully acknowledge the research support of TÜBİTAK via grant 1001-107K241.

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Kidney exchange: An egalitarian mechanism

Abstract

J. Econ. Theory

Kidney International

J. Econ. Theory

Amer. J. Transp.

Games Econ. Behav.

Games Econ. Behav.

Games Econ. Behav.

Random serial dictatorship and the core from random endowments in house allocation problems

Econometrica

Tres observaciones sobre el algebra lineal

Univ. Nac. Tucuman Rev. Ser. A

A simple random assignment problem with a unique solution

Econ. Theory

Random matching under dichotomous preferences

Econometrica

Exchanging kidneys: Advances in living-donor transplantations

New England J. Med.

A concept of egalitarianism under participation constraints

Econometrica

Paths, trees, and flowers

Canad. J. Math.

Maximale systeme Unabhängiger Kanten

Magyar Tud. Akad. Mat. Kutató Int. Köz.