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 Θ(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.
The authors acknowledge support from the Danish National Research Foundation and The National Science Foundation of China (under the grant 61061130540) for the Sino-Danish Center for the Theory of Interactive Computation, within which this work was performed. The authors also acknowledge support from the Center for Research in Foundations of Electronic Markets (CFEM), supported by the Danish Strategic Research Council. Jie Zhang also acknowledges support from ERC Advanced Grant 321171 (ALGAME).
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Filos-Ratsikas, A., Frederiksen, S.K.S., Zhang, J. (2014). Social Welfare in One-Sided Matchings: Random Priority and Beyond. In: Lavi, R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44803-8_1
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DOI: https://doi.org/10.1007/978-3-662-44803-8_1
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