Price of Fairness in Kidney Exchange.

Abstract

Kidney exchange provides a life-saving alternative to long waiting lists for patients in need of a new kidney. Fielded exchanges typically match under utilitarian or near-utilitarian rules; this approach marginalizes certain classes of patients. In this paper, we focus on improving access to kidneys for highly-sensitized, or hard-tomatch, patients. Toward this end, we formally adapt a recently introduced measure of the tradeoff between fairness and efficiencythe price of fairness-to the standard kidney exchange model. We show that the price of fairness in the standard theoretical model is small. We then introduce two natural definitions of fairness and empirically explore the tradeoff between matching more hard-tomatch patients and the overall utility of a utilitarian matching, on real data from the UNOS nationwide kidney exchange and simulated data from each of the standard kidney exchange distributions.

Nash equilibria in the two-player kidney exchange game

“…then the algorithm can cycle. For instance, in Example 1, when we are in iteration 2 and we do not perform the search as stated in step 17, then we can compute the M 2 -alternating path (1,2,11,10,7,6,5,24,25) that would lead us to M 3 = M 1 , making the algorithm to cycle. …”

“…Change in players' objective functions Investigating different players' utilities is of crucial importance, the literature on the kidney exchange program being rich of examples analyzing different solution selection criteria (e.g., see [11]). A simple extension would be to assume that the players prioritize maximum matchings that maximize "hard-to-match" vertices.…”

Using Deceased-Donor Kidneys to Initiate Chains of Living Donor Kidney Paired Donations

“…2005;Unver 2010;Awasthi and Sandholm 2009;Ashlagi and Roth 2014). These algorithms have been further analyzed: studying the problem of transplantation failures due to rejected matching (Dickerson, Procaccia, and Sandholm 2013); focusing on particular classes of patients (e.g. patients with a very low probability of transplantation) (Dickerson, Procaccia, and Sandholm 2014); analyzing the computational complexity of the problem as ILP (Abraham, Blum, and Sandholm 2007); providing an analysis of the efficacy of altruistic-donor chains (Dickerson, Procaccia, and Sandholm 2012); studying the problem of having long chains of kidney exchanges (Glorie, van de Klundert, and Wagelmans 2014;Anderson et al 2015); providing incentives to compatible pairs to participate in these programs (Nicolò and Rodríguez-Álvarez 2012;Nicolò and Rodríguez-Álvarez 2017;Gentry et al 2007); using altruistic donors to initiate chains of donation (Sonmez and Unver 2014; Rees et al 2009;Manlove and O'malley 2014;Manlove and O'Malley 2015).…”

Combinatorial Hodge theory for equitable kidney paired donation

“…Equity and utility are in competition, as shown in [7] which boosts kidney allocation to highly sensitized patients and tracks the loss of utility. The approach used in [7], called weighted fairness (WF), must specify a priori a disadvantaged group of PD-pairs. The chosen group is given bonus utility per allocation, and then the new utility function is maximized via integer programming methods.…”

“…None of the aforementioned algorithms directly analyze the equity in a kidney exchange. While a few studies such as [7] make strides to help particular groups, none seeks to quantify or eliminate general disparity in a kidney exchange as ours does. Moreover, our algorithm is shown to be competitive with the maximal cardinality of rCM as well as the maximal utility of WF.…”