A theoretical and computational equilibria analysis of a multi-player kidney exchange program

Carvalho, Margarida; Lodi, Andrea

doi:10.1016/j.ejor.2022.05.027

Cited by 10 publications

(8 citation statements)

References 37 publications

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“…The objective is to balance the probability of selection of each pair in the KEP through different metrics such as minimizing the mean absolute deviation of the average probability of being selected in an exchange plan. This work followed preliminary observation by Carvalho and Lodi [10]. The authors show that KEPs can have many solutions maximizing the number of transplants.…”

Section: Related Workmentioning

confidence: 61%

“…The aforementioned fairness notions in KEPs are not exhaustive. For example, related to game theory, Sönmez and Ünver [40], Ashlagi and Roth [3], Carvalho and Lodi [10] and Klimentova et al [23] all cast the fairness component of KEPs in a framework where agents (representing hospitals, regions or countries) aim to have the highest utility for their patients.…”

Section: Related Workmentioning

confidence: 99%

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Adaptation, Comparison and Practical Implementation of Fairness Schemes in Kidney Exchange Programs

St-Arnaud¹,

Carvalho²,

Farnadi³

2022

Preprint

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The privileged treatment for patients suffering from end-stage renal disease is transplantation. In Kidney Exchange Programs (KEPs), each participating patient is registered together with an incompatible donor. Then, KEPs maximize overall patient benefit through donor exchanges. Compatibility requirements can severely restrict these programs, with certain patients waiting long to be selected for an exchange. Thus, the policy governing the selection of exchanges requires a careful balance between fairness in terms of individual access to transplantation and utilitarian criteria (e.g., total number of transplants). In this work, we review several fairness schemes, interpret them in the context of KEPs and describe their weaknesses. To overcome those drawbacks, we propose a novel scheme based on the Nash Social Welfare Program that simultaneously optimizes the fairness and the utilitarian objectives. Because the application of fairness schemes and a utilitarian objective implies solving conic programs of exponential size, we design a decomposition methodology to efficiently run them on KEP instances. Finally, we make an extensive comparison of the different schemes and validate the scalability of our methodology for benchmark instances from the literature.

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Section: Related Workmentioning

confidence: 61%

Section: Related Workmentioning

confidence: 99%

Adaptation, Comparison and Practical Implementation of Fairness Schemes in Kidney Exchange Programs

St-Arnaud¹,

Carvalho²,

Farnadi³

2022

Preprint

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“…However, Abraham, Blum and Sandholm [1] proved that already for ℓ = 3 it becomes NP-hard to find an optimal solution for a round. We therefore set ℓ = 2 1 , just like some related papers [14,15,35], which we discuss later.…”

Section: An Application Of Partitioned Matching Gamesmentioning

confidence: 99%

“…To ensure stability, Carvalho and Lodi [14] used a 2-round system with 2-way exchanges only: in the first round each country selects an internal matching, and in the second round a maximum matching is selected for the international exchanges. They gave a polynomial-time algorithm for computing a Nash-equilibrium that maximizes the total number of transplants, improving the previously known result of [15] for two countries.…”

Section: An Application Of Partitioned Matching Gamesmentioning

confidence: 99%

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Partitioned Matching Games for International Kidney Exchange

Benedek¹,

Bíró²,

Kern³

et al. 2023

Preprint

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We introduce partitioned matching games as a suitable model for international kidney exchange programmes, where in each round the total number of available kidney transplants needs to be distributed amongst the participating countries in a "fair" way. A partitioned matching game (N, v) is defined on a graph G = (V, E) with an edge weighting w and a partition V = V1 ∪ • • • ∪ Vn. The player set is N = {1, . . . , n}, and player p ∈ N owns the vertices in Vp. The value v(S) of a coalition S ⊆ N is the maximum weight of a matching in the subgraph of G induced by the vertices owned by the players in S. If |Vp| = 1 for all p ∈ N , then we obtain the classical matching game. Let c = max{|Vp| | 1 ≤ p ≤ n} be the width of (N, v). We prove that checking core non-emptiness is polynomial-time solvable if c ≤ 2 but co-NP-hard if c ≤ 3. We do this via pinpointing a relationship with the known class of b-matching games and completing the complexity classification on testing core nonemptiness for b-matching games. With respect to our application, we prove a number of complexity results on choosing, out of possibly many optimal solutions, one that leads to a kidney transplant distribution that is as close as possible to some prescribed fair distribution.

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