Social Welfare in One-Sided Matchings: Random Priority and Beyond
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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
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.
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