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23
Approximate Mechanism Design Without Money
, 2009
"... The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforc ..."
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Cited by 58 (14 self)
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The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
Truthful assignment without money
 In Proceedings of the 11th ACM Conference on Electronic Commerce (EC
, 2010
"... We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal ..."
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Cited by 25 (0 self)
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We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal is to construct a welfare maximizing feasible assignment. In our model of private valuations, motivated by impossibility results, the value and sizes on all jobmachine pairs are public information; however, whether an edge exists or not in the bipartite graph is a job’s private information. That is, the selfish agents in our model are the jobs, and their private information is their edge set. We want to design mechanisms that are truthful without money (henceforth strategyproof), and produce assignments whose welfare
Individual Rationality and Participation in Large Scale, MultiHospital Kidney Exchange
, 2011
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Dynamic Matching via Weighted Myopia with Application to Kidney Exchange
, 2012
"... In many dynamic matching applications—especially highstakes ones—the competitive ratios of priorfree online algorithms are unacceptably poor. The algorithm should take distributional information about possible futures into account in deciding what action to take now. This is typically done by draw ..."
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Cited by 16 (8 self)
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In many dynamic matching applications—especially highstakes ones—the competitive ratios of priorfree online algorithms are unacceptably poor. The algorithm should take distributional information about possible futures into account in deciding what action to take now. This is typically done by drawing sample trajectories of possible futures at each time period, but may require a prohibitively large number of trajectories or prohibitive memory and/or computation to decide what action to take. Instead, we propose to learn potentials of elements (e.g., vertices) of the current problem. Then, at run time, we simply run an offline matching algorithm at each time period, but subtracting out in the objective the potentials of the elements used up in the matching. We apply the approach to kidney exchange. Kidney exchanges enable willing but incompatible patientdonor pairs (vertices) to swap donors. These swaps typically include cycles longer than two pairs and chains triggered by altruistic donors. Fielded exchanges currently match myopically, maximizing the number of patients who get kidneys in an offline fashion at each time period. Myopic matching is suboptimal; the clearing problem is dynamic since patients, donors, and altruists appear and expire over time. We theoretically compare the power of using potentials on increasingly large elements: vertices, edges, cycles, and the entire graph (optimum). Then, experiments show that by learning vertex potentials, our algorithm matches more patients than the current practice of clearing myopically. It scales to exchanges orders of magnitude beyond those handled by the prior dynamic algorithm.
FailureAware Kidney Exchange
, 2013
"... Most algorithmic matches in fielded kidney exchanges do not result in an actual transplant. In this paper, we address the problem of cycles and chains in a proposed match failing after the matching algorithm has committed to them. We show that failureaware kidney exchange can significantly increase ..."
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Cited by 10 (6 self)
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Most algorithmic matches in fielded kidney exchanges do not result in an actual transplant. In this paper, we address the problem of cycles and chains in a proposed match failing after the matching algorithm has committed to them. We show that failureaware kidney exchange can significantly increase the expected number of lives saved (i) in theory, on random graph models; (ii) on real data from kidney exchange match runs between 2010 and 2012; (iii) on synthetic data generated via a model of dynamic kidney exchange. From the computational viewpoint, we design a branchandpricebased optimal clearing algorithm specifically for the probabilistic exchange clearing problem and show that this new solver scales well on large simulated data, unlike prior clearing algorithms.
A random graph model of kidney exchanges: efficiency, individualrationality and incentives
 In ACM Conference on Electronic Commerce (EC
, 2011
"... In kidney exchanges, hospitals share patient lists and receive transplantations. A kidneypaired donation (KPD) mechanism needs to promote full sharing of information about donorpatient pairs, and identify a Pareto efficient outcome that also satisfies participation constraints of hospitals. We in ..."
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Cited by 10 (2 self)
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In kidney exchanges, hospitals share patient lists and receive transplantations. A kidneypaired donation (KPD) mechanism needs to promote full sharing of information about donorpatient pairs, and identify a Pareto efficient outcome that also satisfies participation constraints of hospitals. We introduce a random graph model of the KPD exchange and then fully characterize the structure of the efficient outcome and the expected number of transplantations that can be performed. Random graph theory allows early experimental results to be explained analytically, and enables the study of participation incentives in a methodological way. We derive a squareroot law between the welfare gains from sharing patientdonor pairs in a central pool and the individual sizes of hospitals, illustrating the urgent need for the nationwide expansion of such programs. Finally, we establish through theoretical and computational analysis that enforcing simple individual rationality constraints on the outcome can mitigate the negative impact of strategic behavior by hospitals.
Free Riding and Participation in Large Scale, Multihospital Kidney Exchange
, 2011
"... As multihospital kidney exchange has grown, the set of players has grown from patients and surgeons to include hospitals. Hospitals can enroll only their hardtomatch patientdonor pairs, while conducting easilyarranged exchanges internally. This behavior has already been observed. We show that th ..."
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Cited by 9 (4 self)
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As multihospital kidney exchange has grown, the set of players has grown from patients and surgeons to include hospitals. Hospitals can enroll only their hardtomatch patientdonor pairs, while conducting easilyarranged exchanges internally. This behavior has already been observed. We show that the cost of making it individually rational for hospitals to participate fully is low in almost every large exchange pool (although the worstcase cost is very high), while the cost of failing to guarantee individual rationality could be high, in lost transplants. We identify a mechanism that achieves high efficiency while giving hospitals incentives to reveal all patientdonor pairs. 1
An improved 2agent kidney exchange mechanism
"... Abstract. We study a mechanism design version of matching computation in graphs that models the game played by hospitals participating in pairwise kidney exchange programs. We present a new randomized matching mechanism for two agents which is truthful in expectation and has an approximation ratio o ..."
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Cited by 8 (5 self)
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Abstract. We study a mechanism design version of matching computation in graphs that models the game played by hospitals participating in pairwise kidney exchange programs. We present a new randomized matching mechanism for two agents which is truthful in expectation and has an approximation ratio of 3/2 to the maximum cardinality matching. This is an improvement over a recent upper bound of 2 [Ashlagi et al., EC 2010] and, furthermore, our mechanism beats for the first time the lower bound on the approximation ratio of deterministic truthful mechanisms. We complement our positive result with new lower bounds. Among other statements, we prove that the weaker incentive compatibility property of truthfulness in expectation in our mechanism is necessary; universally truthful mechanisms that have an inclusionmaximality property have In an attempt to address the wide need for kidney transplantation and the scarcity of cadaver kidneys, several countries have launched, or are considering,
Social Welfare in Onesided Matching Markets without Money
"... We study social welfare in onesided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two na ..."
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Cited by 7 (0 self)
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We study social welfare in onesided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent’s utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first nontrivial performance guarantees for these natural mechanisms.
Harnessing the power of two crossmatches
 IN ACM CONFERENCE ON ELECTRONIC COMMERCE (EC
, 2013
"... Kidney exchanges allow incompatible donorpatient pairs to swap kidneys, but each donation must pass three tests: blood, tissue, and crossmatch. In practice a matching is computed based on the first two tests, and then a single crossmatch test is performed for each matched patient. However, if two c ..."
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Cited by 6 (1 self)
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Kidney exchanges allow incompatible donorpatient pairs to swap kidneys, but each donation must pass three tests: blood, tissue, and crossmatch. In practice a matching is computed based on the first two tests, and then a single crossmatch test is performed for each matched patient. However, if two crossmatches could be performed per patient, in principle significantly more successful exchanges could take place. In this paper, we ask: If we were allowed to perform two crossmatches per patient, could we harness this additional power optimally and efficiently? Our main result is a polynomial time algorithm for this problem that almost surely computes optimal — up to lower order terms — solutions on random large kidney exchange instances.