Barter Exchange with Shared Item Valuations

Juan Luque, Sharmila Duppala, John P Dickerson, Aravind Srinivasan

Keywords: Barter Exchanges, Market Algorithms, Dependent Rounding, Allocation Mechanism, Randomized Algorithms

Abstract: In barter exchanges, agents enter seeking to swap their items for other items on their wishlist. We consider a centralized barter exchange with a set of agents and items where each item has a positive value. The goal is to compute a (re)allocation of items maximizing the agents' collective utility subject to each agent's total received value being comparable to their total given value. Many such centralized barter exchanges exist and serve crucial roles; e.g., kidney exchange programs, which are often formulated as variants of directed cycle packing. We show finding a reallocation where each agent's total given and total received values are equal is NP-hard. On the other hand, we develop a randomized algorithm that achieves optimal utility in expectation and where, i) for any agent, with probability 1 their received value is at least their given value minus $v^*$ where $v^*$ is said agent's most valuable owned and wished-for item, and ii) each agent's given and received values are equal in expectation. Our main result is achieved by building on the dependent rounding algorithm of [Gandhi et al. 2006].

Track: Economics, Online Markets, and Human Computation

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Submission Number: 1910