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Private matchings and allocations

Published: 31 May 2014 Publication History

Abstract

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for each good: in this case, the problem is exactly the maximum-weight matching problem in a bipartite graph.
Private matching and allocation problems have not been considered in the differential privacy literature, and for good reason: they are plainly impossible to solve under differential privacy. Informally, the allocation must match agents to their preferred goods in order to maximize social welfare, but this preference is exactly what agents wish to hide! Therefore, we consider the problem under the relaxed constraint of joint differential privacy: for any agent i, no coalition of agents excluding i should be able to learn about the valuation function of agent i. In this setting, the full allocation is no longer published---instead, each agent is told what good to get. We first show that with a small number of identical copies of each good, it is possible to efficiently and accurately solve the maximum weight matching problem while guaranteeing joint differential privacy. We then consider the more general allocation problem, when bidder valuations satisfy the gross substitutes condition. Finally, we prove that the allocation problem cannot be solved to non-trivial accuracy under joint differential privacy without requiring multiple copies of each type of good.

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    cover image ACM Conferences
    STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing
    May 2014
    984 pages
    ISBN:9781450327107
    DOI:10.1145/2591796
    Permission to make digital or hard copies of all or part 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 components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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    Published: 31 May 2014

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    Author Tags

    1. ascending auction
    2. differential privacy
    3. gross substitutes
    4. matching

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    STOC '14: Symposium on Theory of Computing
    May 31 - June 3, 2014
    New York, New York

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    STOC '14 Paper Acceptance Rate 91 of 319 submissions, 29%;
    Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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    Cited By

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    • (2024)Differentially private no-regret exploration in adversarial Markov decision processesProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702687(235-272)Online publication date: 15-Jul-2024
    • (2024)Stable Task Assignment with Range Partition under Differential PrivacyDatabase Systems for Advanced Applications10.1007/978-981-97-5562-2_16(243-253)Online publication date: 27-Oct-2024
    • (2023)Differentially Private Resource AllocationProceedings of the 39th Annual Computer Security Applications Conference10.1145/3627106.3627181(772-786)Online publication date: 4-Dec-2023
    • (2023)A Game-Theoretic Federated Learning Framework for Data Quality ImprovementIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.323095935:11(10952-10966)Online publication date: 1-Nov-2023
    • (2023)A Robust Game-Theoretical Federated Learning Framework With Joint Differential PrivacyIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2021.314013135:4(3333-3346)Online publication date: 1-Apr-2023
    • (2022)A Distributed Differentially Private Algorithm for Resource Allocation in Unboundedly Large SettingsProceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems10.5555/3535850.3535888(327-335)Online publication date: 9-May-2022
    • (2021)Differentially private model personalizationProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3542536(29723-29735)Online publication date: 6-Dec-2021
    • (2021)More than PrivacyACM Computing Surveys10.1145/346077154:7(1-37)Online publication date: 18-Jul-2021
    • (2021)Computing Payoff Allocations in the Approximate Core of Linear Programming Games in a Privacy-Preserving MannerOperations Research Letters10.1016/j.orl.2021.12.008Online publication date: Dec-2021
    • (2020)The Possibilities and Limitations of Private Prediction MarketsACM Transactions on Economics and Computation10.1145/34123488:3(1-24)Online publication date: 25-Sep-2020
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