A coverage function f over a ground set [m] is associated with a universe U
of weighted elements and m subsets A_1,..., A_m of U, and for any subset T of
[m], f(T) is defined as the total weight of the elements in the union
$\cup_{j\in T} A_j$. Coverage functions are an important special case of
submodular functions, and arise in many applications, for instance as a class
of utility functions of agents in combinatorial auctions.
We study the multi-parameter mechanism design problem in Bayesian setting.
The mechanism design problem for social welfare is solved optimally by the
well-known VCG mechanism even in the prior-free setting. One of the major
weaknesses of VCG is that it is not computationally efficient in general. And
the natural approaches that use VCG-like mechanisms based on approximation
allocation algorithm fail to preserve incentive compatibility. Very recently,
Hartline and Lucier study the single-parameter mechanism design problem for
social welfare in Bayesian setting.