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Average-case analysis of the assignment problem with independent preferences

Average-case analysis of the assignment problem with independent preferences
Average-case analysis of the assignment problem with independent preferences
The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism \textit{Random Priority} is asymptotically the best mechanism for this purpose, when comparing its welfare to the optimal social welfare using the canonical \textit{worst-case approximation ratio}. Despite its popularity, the efficiency loss indicated by the worst-case ratio does not have a constant bound. Recently, [Deng, Gao, Zhang 2017] show that when the agents' preferences are drawn from a uniform distribution, its \textit{average-case approximation ratio} is upper bounded by 3.718. They left it as an open question of whether a constant ratio holds for general scenarios. In this paper, we offer an affirmative answer to this question by showing that the ratio is bounded by 1/μ when the preference values are independent and identically distributed random variables, where μ is the expectation of the value distribution. This upper bound also improves the upper bound of 3.718 in [Deng, Gao, Zhang 2017] for the Uniform distribution. Moreover, under mild conditions, the ratio has a \textit{constant} bound for any independent random values. En route to these results, we develop powerful tools to show the insights that in most instances the efficiency loss is small.
Gao, Yansong
203d3e45-b3e2-4e34-8632-c10ac44d6ccd
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Gao, Yansong
203d3e45-b3e2-4e34-8632-c10ac44d6ccd
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Gao, Yansong and Zhang, Jie (2019) Average-case analysis of the assignment problem with independent preferences. 13 pp .

Record type: Conference or Workshop Item (Paper)

Abstract

The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism \textit{Random Priority} is asymptotically the best mechanism for this purpose, when comparing its welfare to the optimal social welfare using the canonical \textit{worst-case approximation ratio}. Despite its popularity, the efficiency loss indicated by the worst-case ratio does not have a constant bound. Recently, [Deng, Gao, Zhang 2017] show that when the agents' preferences are drawn from a uniform distribution, its \textit{average-case approximation ratio} is upper bounded by 3.718. They left it as an open question of whether a constant ratio holds for general scenarios. In this paper, we offer an affirmative answer to this question by showing that the ratio is bounded by 1/μ when the preference values are independent and identically distributed random variables, where μ is the expectation of the value distribution. This upper bound also improves the upper bound of 3.718 in [Deng, Gao, Zhang 2017] for the Uniform distribution. Moreover, under mild conditions, the ratio has a \textit{constant} bound for any independent random values. En route to these results, we develop powerful tools to show the insights that in most instances the efficiency loss is small.

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More information

Accepted/In Press date: 2019
Published date: 2019

Identifiers

Local EPrints ID: 431996
URI: http://eprints.soton.ac.uk/id/eprint/431996
PURE UUID: 24e101fa-fd40-4f6b-938f-d773bc926737
ORCID for Jie Zhang: ORCID iD orcid.org/0000-0002-5348-7671

Catalogue record

Date deposited: 26 Jun 2019 16:30
Last modified: 26 Nov 2021 03:10

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Contributors

Author: Yansong Gao
Author: Jie Zhang ORCID iD

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