  We study procurement games where each seller supplies multiple units of his
item, with a cost per unit known only to him. The buyer can purchase any number
of units from each seller, values different combinations of the items
differently, and has a budget for his total payment.
  For a special class of procurement games, the {\em bounded knapsack} problem,
we show that no universally truthful budget-feasible mechanism can approximate
the optimal value of the buyer within $\ln n$, where $n$ is the total number of
units of all items available. We then construct a polynomial-time mechanism
that gives a $4(1+\ln n)$-approximation for procurement games with {\em concave
additive valuations}, which include bounded knapsack as a special case. Our
mechanism is thus optimal up to a constant factor. Moreover, for the bounded
knapsack problem, given the well-known FPTAS, our results imply there is a
provable gap between the optimization domain and the mechanism design domain.
  Finally, for procurement games with {\em sub-additive valuations}, we
construct a universally truthful budget-feasible mechanism that gives an
$O(\frac{\log^2 n}{\log \log n})$-approximation in polynomial time with a
demand oracle.
