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  1. null (Ed.)
  2. null (Ed.)
    We consider the problem of selling perishable items to a stream of buyers in order to maximize social welfare. A seller starts with a set of identical items, and each arriving buyer wants any one item, and has a valuation drawn i.i.d. from a known distribution. Each item, however, disappears after an a priori unknown amount of time that we term the horizon for that item. The seller knows the (possibly different) distribution of the horizon for each item, but not its realization till the item actually disappears. As with the classic prophet inequalities, the goal is to design an online pricing scheme that competes with the prophet that knows the horizon and extracts full social surplus (or welfare). Our main results are for the setting where items have independent horizon distributions satisfying the monotone-hazard-rate (MHR) condition. Here, for any number of items, we achieve a constant-competitive bound via a conceptually simple policy that balances the rate at which buyers are accepted with the rate at which items are removed from the system. We implement this policy via a novel technique of matching via probabilistically simulating departures of the items at future times. Moreover, for a single item and MHR horizon distribution with mean, we show a tight result: There is a fixed pricing scheme that has competitive ratio at most 2 - 1/μ, and this is the best achievable in this class. We further show that our results are best possible. First, we show that the competitive ratio is unbounded without the MHR assumption even for one item. Further, even when the horizon distributions are i.i.d. MHR and the number of items becomes large, the competitive ratio of any policy is lower bounded by a constant greater than 1, which is in sharp contrast to the setting with identical deterministic horizons. 
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  3. A core tension in the operations of online marketplaces is between segmentation (wherein platforms can increase revenue by segmenting the market into ever smaller sub-markets) and thickness (wherein the size of the sub-market affects the utility experienced by an agent). An important example of this is in dynamic online marketplaces, where buyers and sellers, in addition to preferences for different matches, also have finite patience (or deadlines) for being matched. We formalize this trade-off via a novel optimization problem that we term as 'Two-sided Facility Location': we consider a market wherein agents arrive at nodes embedded in an underlying metric space, where the distance between a buyer and seller captures the quality of the corresponding match. The platform posts prices and wages at the nodes, and opens a set of virtual clearinghouses where agents are routed for matching. To ensure high match-quality, the platform imposes a distance constraint between an agent and its clearinghouse; to ensure thickness, the platform requires the flow to any clearinghouse be at least a pre-specified lower bound. Subject to these constraints, the goal of the platform is to maximize the social surplus subject to weak budget balance, i.e., profit being non-negative. Our work characterizes the complexity of this problem by providing both hardness results as well as algorithms for this setting; in particular, we present an algorithm that for any constant ε > 0 yields a (1 + ε ) approximation for the gains from trade, while relaxing the match quality (i.e., maximum distance of any match) by a constant factor. 
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