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arXiv · 1403.1508

Social welfare in one-sided matchings: Random priority and beyond

Aris Filos-Ratsikas·Søren Kristoffer Stiil Frederiksen·Jie Zhang
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Abstract

We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known truthful-in-expectation mechanism for the problem. We prove that the approximation ratio of random priority is Theta(n^{-1/2}) while no truthful-in-expectation mechanism can achieve an approximation ratio better than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we prove that the approximation ratio of all ordinal (not necessarily truthful-in-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating that random priority is asymptotically the best truthful-in-expectation mechanism and the best ordinal mechanism for the problem.

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Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Jie Zhang. 2014-03-06. Social welfare in one-sided matchings: Random priority and beyond. https://arxiv.org/abs/1403.1508

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