3 research outputs found
Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching
We study the efficiency (in terms of social welfare) of truthful and
symmetric mechanisms in one-sided matching problems with {\em dichotomous
preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are
particularly interested in the well-known {\em 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(\opt)^2}{n}, where \nu(\opt) is the maximum social
welfare and 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(\opt)^2}{n}.Comment: 13 pages, 1 figur
Social Welfare in One-Sided Matching Mechanisms
We study the Price of Anarchy of mechanisms for the well-known problem of
one-sided matching, or house allocation, with respect to the social welfare
objective. We consider both ordinal mechanisms, where agents submit preference
lists over the items, and cardinal mechanisms, where agents may submit
numerical values for the items being allocated. We present a general lower
bound of on the Price of Anarchy, which applies to all
mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and
Random Priority, achieve a matching upper bound. We extend our lower bound to
the Price of Stability of a large class of mechanisms that satisfy a common
proportionality property, and show stronger bounds on the Price of Anarchy of
all deterministic mechanisms