Predict and Match: Prophet Inequalities with Uncertain Supply
Authors: 
Reza Alijani, Siddhartha Banerjee, Sreenivas Gollapudi, Kamesh Munagala, Kangning WangAuthors Info & Claims
Reza Alijani, Siddhartha Banerjee, Sreenivas Gollapudi, Kamesh Munagala, Kangning WangAuthors Info & ClaimsPages 13 - 14
Abstract
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 μ, 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.
Supplementary Material
This is the presentation for "Predict and Match: Prophet Inequalities with Uncertain Supply" accepted to SIGMETRICS 2020. 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).\r\n
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Published In
June 2020
124 pages
ISBN:9781450379854
DOI:10.1145/3393691
- General Chair:
- Edmund Yeh,
- Program Chairs:
- Athina Markopoulou,
- Y.C. Tay
Copyright © 2020 Owner/Author.
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.
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Association for Computing Machinery
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Published: 08 June 2020
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SIGMETRICS '20
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SIGMETRICS '20: ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems
June 8 - 12, 2020
MA, Boston, USA
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Overall Acceptance Rate 459 of 2,691 submissions, 17%
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