Pareto stability in matching marketplaces

Motivated by online matching marketplaces such as social lending, we study markets where capacity-constrained bidders participate in multiple auctions that they have preferences over. While bidders have explicit preferences over auctions, we observe that the auctioneer side of the market has implicit preferences over bidders induced by the bids; this allows us to model these marketplaces in a matching framework with two-sided preferences. The problem of clearing the market leads naturally to the algorithmic question of computing Pareto-optimal stable matchings in a many-to-many setting with ties and incomplete lists. We will provide a fast algorithm for computing Pareto-stable assignments for this very general multi-unit matching problem with arbitrary preference lists on both sides, with running time that is polynomial in the number of agents in the market, rather than the sum of capacities of all agents.