Efficiency of Truthful and Symmetric Mechanisms in One-Sided Matching

Abstract

We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with dichotomous preferences and normalized von Neumann-Morgenstern preferences. We are particularly interested in the well-known Random Serial Dictatorship mechanism. For dichotomous preferences, we first show that truthful, symmetric and optimal mechanisms exist if intractable mechanisms are allowed. We then provide a connection to online bipartite matching. Using this connection, it is possible to design truthful, symmetric and tractable mechanisms that extract 0.69 of the maximum social welfare, which works under assumption that agents are not adversarial. Without this assumption, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least a third of the maximum social welfare. For normalized von Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least $\frac{1}{e}\frac{\nu(\mathcal{O})^2}{n}$, where $\nu(\mathcal{O})$ is the maximum social welfare and n is the number of both agents and items. On the hardness side, we show that no truthful mechanism can achieve a social welfare better than $\frac{\nu(\mathcal{O})^2}{n}$.

This work was partially supported by ERC StG project PAAl 259515, FET IP project MULTIPEX 317532, and NCN grant N N206 567940.