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Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design

Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design
Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design

A mechanism for the random assignment problem takes agents' private preferences over items as input and outputs an allocation. One of the mainstream mechanisms, Random Priority, is asymptotically the best mechanism for welfare maximization. However, its approximation ratio is Θ(n), which implies that there is a large discrepancy between its performance and the optimal social welfare. We evaluate the performance of Random Priority beyond the worst-case analysis in the hope of addressing the inconsistency between the widespread use of the mechanism in practice and the undesired theoretical performance guarantee. We show that with small random noise applied to the worst-case inputs, Random Priority has a constant smoothed approximation ratio. When agents' preference values are independent random variables, Random Priority is nearly optimal evaluated by the average-case approximation ratio. En route to these results, we develop analytics tools to show the insights that the efficiency loss is small on most instances. To our limited knowledge, this is the first work that introduces smoothed analysis to algorithmic mechanism design problems. These results may pave the way for further studies for approximate mechanism design problems beyond the worst-case analysis.

Approximation ratio, Average-case analysis, Mechanism design, Smoothed analysis
0890-5401
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Gao, Yansong
203d3e45-b3e2-4e34-8632-c10ac44d6ccd
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Gao, Yansong
203d3e45-b3e2-4e34-8632-c10ac44d6ccd
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Deng, Xiaotie, Gao, Yansong and Zhang, Jie (2022) Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design. Information and Computation, 285, [104920]. (doi:10.1016/j.ic.2022.104920).

Record type: Article

Abstract

A mechanism for the random assignment problem takes agents' private preferences over items as input and outputs an allocation. One of the mainstream mechanisms, Random Priority, is asymptotically the best mechanism for welfare maximization. However, its approximation ratio is Θ(n), which implies that there is a large discrepancy between its performance and the optimal social welfare. We evaluate the performance of Random Priority beyond the worst-case analysis in the hope of addressing the inconsistency between the widespread use of the mechanism in practice and the undesired theoretical performance guarantee. We show that with small random noise applied to the worst-case inputs, Random Priority has a constant smoothed approximation ratio. When agents' preference values are independent random variables, Random Priority is nearly optimal evaluated by the average-case approximation ratio. En route to these results, we develop analytics tools to show the insights that the efficiency loss is small on most instances. To our limited knowledge, this is the first work that introduces smoothed analysis to algorithmic mechanism design problems. These results may pave the way for further studies for approximate mechanism design problems beyond the worst-case analysis.

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More information

Published date: May 2022
Additional Information: Funding Information: Xiaotie Deng was supported by Science and Technology Innovation 2030 – “New Generation Artificial Intelligence” Major Project (No. 2018AAA0100901 ) and the National Natural Science Foundation of China (Grant No. 62172012 ). Jie Zhang was supported by a Leverhulme Trust Research Project Grant (2021 – 2024). Publisher Copyright: © 2022 The Author(s)
Keywords: Approximation ratio, Average-case analysis, Mechanism design, Smoothed analysis

Identifiers

Local EPrints ID: 469839
URI: http://eprints.soton.ac.uk/id/eprint/469839
ISSN: 0890-5401
PURE UUID: 6fe7f062-ff9f-4e8e-ae6b-5ecf1e30a042

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Date deposited: 27 Sep 2022 16:37
Last modified: 27 Sep 2022 16:37

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Contributors

Author: Xiaotie Deng
Author: Yansong Gao
Author: Jie Zhang

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