A Unified Approach to Dynamic Matching and Barter Exchange

Abstract : The exchange of indivisible goods without money addresses a variety of constrained economic settings where a medium of exchange such as money is considered inappropriate. Participants are either matched directly with another participant or, in more complex domains, in barter cycles and chains with many other participants before exchanging their endowed goods. This thesis addresses the design, analysis, and real-world fielding of dynamic matching markets and barter exchanges. We present new mathematical models for static and dynamic barter exchange that more accurately reflect reality, prove theoretical statements about the characteristics and behavior of these markets, and develop provably optimal market clearing algorithms for models of these markets that can be deployed in practice. We show that taking a holistic approach to balancing efficiency and fairness can often practically circumvent negative theoretical results. We support the theoretical claims made in this thesis with extensive experiments on data from the United Network for Organ Sharing(UNOS) Kidney Paired Donation Pilot Program, a large kidney exchange clearinghouse in the US with which we have been actively involved. Specifically, we study three competing dimensions found in both matching markets and barter exchange: uncertainty over the existence of possible trades (represented as edges in a graph constructed from participants in the market), balancing efficiency and fairness, and inherent dynamism. For each individual dimension, we provide new theoretical insights as to the effect on market efficiency and match composition of clearing markets under models that explicitly consider those dimensions. We support each theoretical construct with new optimization models and techniques, and validate them on simulated and real kidney exchange data.