  An important research thread in algorithmic game theory studies the design of
efficient truthful mechanisms that approximate the optimal social welfare. A
fundamental question is whether an \alpha-approximation algorithm translates
into an \alpha-approximate truthful mechanism. It is well-known that plugging
an \alpha-approximation algorithm into the VCG technique may not yield a
truthful mechanism. Thus, it is natural to investigate properties of
approximation algorithms that enable their use in truthful mechanisms.
  The main contribution of this paper is to identify a useful and natural
property of approximation algorithms, which we call loser-independence; this
property is applicable in the single-minded and single-parameter settings.
Intuitively, a loser-independent algorithm does not change its outcome when the
bid of a losing agent increases, unless that agent becomes a winner. We
demonstrate that loser-independent algorithms can be employed as sub-procedures
in a greedy iterative packing approach while preserving monotonicity. A greedy
iterative approach provides a good approximation in the context of maximizing a
non-decreasing submodular function subject to independence constraints. Our
framework gives rise to truthful approximation mechanisms for various problems.
Notably, some problems arise in online mechanism design.
