  In this paper, we focus our attention on the large capacities unsplittable
flow problem in a game theoretic setting. In this setting, there are selfish
agents, which control some of the requests characteristics, and may be
dishonest about them. It is worth noting that in game theoretic settings many
standard techniques, such as randomized rounding, violate certain monotonicity
properties, which are imperative for truthfulness, and therefore cannot be
employed. In light of this state of affairs, we design a monotone deterministic
algorithm, which is based on a primal-dual machinery, which attains an
approximation ratio of $\frac{e}{e-1}$, up to a disparity of $\epsilon$ away.
This implies an improvement on the current best truthful mechanism, as well as
an improvement on the current best combinatorial algorithm for the problem
under consideration. Surprisingly, we demonstrate that any algorithm in the
family of reasonable iterative path minimizing algorithms, cannot yield a
better approximation ratio. Consequently, it follows that in order to achieve a
monotone PTAS, if exists, one would have to exert different techniques. We also
consider the large capacities \textit{single-minded multi-unit combinatorial
auction problem}. This problem is closely related to the unsplittable flow
problem since one can formulate it as a special case of the integer linear
program of the unsplittable flow problem. Accordingly, we obtain a comparable
performance guarantee by refining the algorithm suggested for the unsplittable
flow problem.
