Superiority of Instantaneous Decisions in Thin Dynamic Matching Markets

We study a dynamic matching procedure where homogeneous agents arrive at random according to a Poisson process and form edges at random yielding a sparse market. Agents leave according to a certain departure distribution and may leave early by forming a pair with a compatible agent. The primary objective is to maximize the number of matched agents. Our main result is to show that a mild condition on the departure distribution suffices to get almost optimal performance of instantaneous matching, despite operating in a thin market. We are thus the first to provide a natural condition under which instantaneous decisions are superior in a market that is both sparse and thin. This result is surprising because similar results in the previous literature are based on market thickness. In addition, instantaneous matching performs well with respect to further objectives such as minimizing waiting times and avoiding the risk of market congestion. We develop new techniques for proving our results going beyond commonly adopted methods for Markov processes.Comment: Appears in the 24th ACM Conference on Economics and Computation (EC), 202

Dynamic Matching Market Design

We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three perspectives: waiting, optimization, and information. The main insight of our analysis is that waiting to thicken the market can be substantially more important than increasing the speed of transactions, and this is quite robust to the presence of waiting costs. From an optimization perspective, naive local algorithms, that choose the right time to match agents but do not exploit global network structure, can perform very close to optimal algorithms. From an information perspective, algorithms that employ even partial information on agents' departure times perform substantially better than those that lack such information. To elicit agents' departure times, we design an incentive-compatible continuous-time dynamic mechanism without transfers

A dynamic model of barter exchange

We consider the problem of efficient operation of a barter exchange platform for indivisible goods. We introduce a dynamic model of barter exchange where in each period one agent arrives with a single item she wants to exchange for a different item. We study a homogeneous and stochastic environment: an agent is interested in the item possessed by another agent with probability p, independently for all pairs of agents. We consider two settings with respect to the types of allowed exchanges: a) Only two-way cycles, in which two agents swap their items, b) Two or three-way cycles. The goal of the platform is to minimize the average waiting time of an agent. Somewhat surprisingly, we find that in each of these settings, a policy that conducts exchanges in a greedy fashion is near optimal, among a large class of policies that includes batching policies. Further, we find that for small p, allowing three-cycles can greatly improve the waiting time over the two-cycles only setting. Specifically, we find that a greedy policy achieves an average waiting time of Θ(1/p2) in setting a), and Θ(1/p3/2) in setting b). Thus, a platform can achieve the smallest waiting times by using a greedy policy, and by facilitating three cycles, if possible. Our findings are consistent with empirical and computational observations which compare batching policies in the context of kidney exchange programs

Essays in Econometrics and Dynamic Kidney Exchange

Thesis advisor: Stefan HoderleinThis dissertation is divided into two parts. Part I - Dynamic Kidney Exchange In recent years, kidney paired donation (KPD) has an emerged as an attractive alternative for end-stage renal disease patients with incompatible living donors. However, we argue that the matching algorithm currently used by organ clearinghouses is inefficient, in the sense that a larger number of patients may be reached if kidney transplant centers take into consideration how their pool of patients and donors will evolve over time. In our work Two Novel Algorithms for Dynamic Kidney Exchange, we explore this claim and propose new computational algorithms to increase the cardinality of matchings in a discrete-time dynamic kidney exchange model with Poisson entries and Geometric deaths. Our algorithms are classified into direct prediction methods and multi-armed bandit methods. In the direct prediction method, we use machine learning estimator to produce a probability that each patient-donor pair should be matched today, as op- posed to being left for a future matching. The estimators are trained on offline optimal solutions. In contrast, in multi-armed bandit methods, we use simulations to evaluate the desirability of different matchings. Since the amount of different matchings is enormous, multi-armed bandits (MAB) are employed to decrease order to decrease the computational burden. Our methods are evaluated using simulations in a variety of simulation configurations. We find that the performance of at least one of our methods, based on multi-armed bandit algorithms, is able to uniformly dominate the myopic method that is used by kidney transplants in practice. We restrict our experiments to pairwise kidney exchange, but the methods described here are easily extensible, computational constraints permitting. Part II - Econometrics In our econometric paper Heterogenous Production Functions, Panel Data, and Productivity, we present methods for identification of moments and nonparametric marginal distributions of endogenous random coefficient models in fixed-T linear panel data models. Our identification strategy is constructive, immediately leading to relatively simple estimators that can be shown to be consistent and asymptotically normal. Because our strategy makes use of special properties of “small” (measure-zero) subpopulations, our estimators are irregularly identified: they can be shown to be consistent and asymptotically Normal, but converge at rates slower than root-n. We provide an illustration of our methods by estimating first and second moments of random Cobb-Douglas coefficients in production functions, using Indian plant-level microdata.Thesis (PhD) — Boston College, 2018.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Economics

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