Scalable Robust Kidney Exchange

In barter exchanges, participants directly trade their endowed goods in a constrained economic setting without money. Transactions in barter exchanges are often facilitated via a central clearinghouse that must match participants even in the face of uncertainty---over participants, existence and quality of potential trades, and so on. Leveraging robust combinatorial optimization techniques, we address uncertainty in kidney exchange, a real-world barter market where patients swap (in)compatible paired donors. We provide two scalable robust methods to handle two distinct types of uncertainty in kidney exchange---over the quality and the existence of a potential match. The latter case directly addresses a weakness in all stochastic-optimization-based methods to the kidney exchange clearing problem, which all necessarily require explicit estimates of the probability of a transaction existing---a still-unsolved problem in this nascent market. We also propose a novel, scalable kidney exchange formulation that eliminates the need for an exponential-time constraint generation process in competing formulations, maintains provable optimality, and serves as a subsolver for our robust approach. For each type of uncertainty we demonstrate the benefits of robustness on real data from a large, fielded kidney exchange in the United States. We conclude by drawing parallels between robustness and notions of fairness in the kidney exchange setting.Comment: Presented at AAAI1

Paired and altruistic kidney donation in the UK: Algorithms and experimentation

We study the computational problem of identifying optimal sets of kidney exchanges in the UK. We show how to expand an integer programming-based formulation due to Roth et al. [2007] in order to model the criteria that constitute the UK definition of optimality. The software arising from this work has been used by the National Health Service Blood and Transplant to find optimal sets of kidney exchanges for their National Living Donor Kidney Sharing Schemes since July 2008. We report on the characteristics of the solutions that have been obtained in matching runs of the scheme since this time. We then present empirical results arising from experiments on the real datasets that stem from these matching runs, with the aim of establishing the extent to which the particular optimality criteria that are present in the UK influence the structure of the solutions that are ultimately computed. A key observation is that allowing four-way exchanges would be likely to lead to a moderate number of additional transplants

Beyond Gift and Bargain: Some Suggestions for Increasing Kidney Exchanges

Each year, thousands of people in the United States die from end stage renal disease (ESRD), despite the fact that we have the medical knowledge necessary to save them. The reason is simple: these people need a kidney transplant and we have too few kidneys. Given our current technology, the only way to meet the massive annual shortfall between the number of kidneys that are donated and the number of kidneys that are necessary to save the lives of those with ESRD is to increase the number of living donations. The debate on how to do so has often pitted those who favor creating a “free market” in human organs against those who believe that the selling of organs by human donors poses unacceptable evils and risks. Current law prohibits donors from being paid for kidneys. Once the donation has been made, however, the kidney will often change hands in exchange for money several times before reaching the patient. There are no serious proposals to ban such transactions. This article generally sympathizes with those who favor the free alienation of kidneys by donors in exchange for payment. The goal of this article, however, is not to make another charge across the no man’s land separating free-marketeers from prohibitionists. Rather, it aims to explore ways in which we can increase trust in order to foster a promising new development in transplant medicine: extended kidney exchange

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Existing exact solution methods for KEP either are designed for the case where only cyclic exchanges are considered, or can handle long chains but are scalable as long as cycles are short. We develop the first decomposition method that is able to deal with long cycles and long chains for large realistic instances. More specifically, we propose a branch-and-price framework, in which the pricing problems are solved (for the first time in packing problems in a digraph) through multi-valued decision diagrams. Also, we present a new upper bound on the optimal value of KEP, stronger than the one proposed in the literature, which is obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths

Minimalist Market Design: A Framework for Economists with Policy Aspirations

Earlier in my career, prevalent approaches in the emerging field of market design largely represented the experiences and perspectives of leaders who were commissioned to design or reform various institutions. Since being commissioned for a similar task seemed unlikely for me as an aspiring design economist, I developed my own minimalist approach to market design. Using the policy objectives of stakeholders, my approach creates a new institution from the existing one with minimal interference with its elements that compromise the objectives. Minimalist market design initially evolved through my integrated research and policy efforts in school choice from 1997 to 2005 and in kidney exchange from 2003 to 2007. Given its success in school choice and kidney exchange, I systematically followed this approach in many other, often unusual real-world settings. In recent years, my efforts in minimalist market design led to the 2021 reform of the US Army's branching system for its cadets to military specialties, the adoption of reserve systems during the Covid-19 pandemic for vaccine allocation in 15 states and therapies in 2 states, and the deployment of a highly efficient liver exchange system in T\"urkiye. This same methodology also predicted the rescission of a 1995 Supreme Court judgment in India, resulting in countless litigations and interruptions of public recruitment for 25 years, as well as the mandates of its replacement. In this monograph, I describe the philosophy, evolution, and successful applications of minimalist market design, contrasting it with the mainstream paradigm for the field. In doing so, I also provide a paradigm for economists who want to influence policy and change institutions through their research

Making apartments affordable: moving from speculative to deliberative development

Urban consolidation policies in Australia presuppose apartments as the new dominant housing type, but much of what the market has delivered is criticised as over-development, and as being generic, poorly-designed, environmentally unsustainable and unaffordable. In contrast to the usual focus on planning regulation and construction costs as the primary issues needing to be addressed in order to increase the supply of quality, affordable apartment housing this paper uses Ball’s (1983) ‘structure of provision’ approach to outline the key processes informing apartment development to reveal a substantial gap in critical understanding of how apartments are developed in Australia, and identifies economic problems not previously considered by policymakers. Using mainstream economic analysis to review the market itself, the authors found high search costs, demand risk, problems with exchange, and lack of competition present key barriers to achieving greater affordability and limit the extent to which ‘speculative’ developers can respond to the preferences of would be owner-occupiers of apartments. The existing development model, which is reliant on capturing uplift in site value, suits investors seeking rental yields in the first instance and capital gains in the second instance, and actively encourages housing price inflation. This is exacerbated by lack of density restrictions, such as have existed in inner Melbourne for many years, which permits greater yields on redevelopment sites. The price of land in the vicinity of such redevelopment sites is pushed up as landholders\u27 expectation of future yield is raised. All too frequently existing redevelopment sites go back onto the market as vendors seek to capture the uplift in site value and exit the project in a risk free manner. The paper proposes three major reforms. Firstly, that the market for apartment development be re-designed following insights from the economic field of ‘Market Design’ (a branch of Game Theory). A two-sided matching market for new apartments is proposed, where demand-side risks can be mitigated via consumer aggregation. Secondly, consumers should be empowered through support for  ‘deliberative’, or ‘do-it-yourself’ (DYI) development models, in order to increase competition, expand access, and promote responsiveness to consumer needs and preferences. Finally, planning schemes need to impose density restrictions (in the form of height limits, floor space ratios or bedroom quotas) in localities where housing demand is high, in order to dampen speculation and de-risk development by creating certainty. However restrictions on over-development on larger infill sites needs to be offset by permitting intensification of ‘greyfield’ suburbs. Aggregating existing housing lots to enable precinct regeneration and moderate height and density increases would permit better use of airspace thus allowing design outcomes that can optimise land use while retaining amenity

Matching under Preferences

Matching theory studies how agents and/or objects from different sets can be matched with each other while taking agents\u2019 preferences into account. The theory originated in 1962 with a celebrated paper by David Gale and Lloyd Shapley (1962), in which they proposed the Stable Marriage Algorithm as a solution to the problem of two-sided matching. Since then, this theory has been successfully applied to many real-world problems such as matching students to universities, doctors to hospitals, kidney transplant patients to donors, and tenants to houses. This chapter will focus on algorithmic as well as strategic issues of matching theory. Many large-scale centralized allocation processes can be modelled by matching problems where agents have preferences over one another. For example, in China, over 10 million students apply for admission to higher education annually through a centralized process. The inputs to the matching scheme include the students\u2019 preferences over universities, and vice versa, and the capacities of each university. The task is to construct a matching that is in some sense optimal with respect to these inputs. Economists have long understood the problems with decentralized matching markets, which can suffer from such undesirable properties as unravelling, congestion and exploding offers (see Roth and Xing, 1994, for details). For centralized markets, constructing allocations by hand for large problem instances is clearly infeasible. Thus centralized mechanisms are required for automating the allocation process. Given the large number of agents typically involved, the computational efficiency of a mechanism's underlying algorithm is of paramount importance. Thus we seek polynomial-time algorithms for the underlying matching problems. Equally important are considerations of strategy: an agent (or a coalition of agents) may manipulate their input to the matching scheme (e.g., by misrepresenting their true preferences or underreporting their capacity) in order to try to improve their outcome. A desirable property of a mechanism is strategyproofness, which ensures that it is in the best interests of an agent to behave truthfully

Randomized Parameterized Algorithms for the Kidney Exchange Problem

In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney exchange problem plays a critical role. The graph theory model of the kidney exchange problem is to find a maximum weight packing of vertex-disjoint cycles and chains for a given weighted digraph. In general, the length of cycles is not more than a given constant L (typically 2 L 5), and the objective function corresponds to maximizing the number of possible kidney transplants. In this paper, we study the parameterized complexity and randomized algorithms for the kidney exchange problem without chains from theory. We construct two different parameterized models of the kidney exchange problem for two cases L = 3 and L 3, and propose two randomized parameterized algorithms based on the random partitioning technique and the randomized algebraic technique, respectively