  Some important classical mechanisms considered in Microeconomics and Game
Theory require the solution of a difficult optimization problem. This is true
of mechanisms for combinatorial auctions, which have in recent years assumed
practical importance, and in particular of the gold standard for combinatorial
auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these
mechanisms - in particular, their truth revelation properties - assumes that
the optimization problems are solved precisely. In reality, these optimization
problems can usually be solved only in an approximate fashion. We investigate
the impact on such mechanisms of replacing exact solutions by approximate ones.
Specifically, we look at a particular greedy optimization method. We show that
the GVA payment scheme does not provide for a truth revealing mechanism. We
introduce another scheme that does guarantee truthfulness for a restricted
class of players. We demonstrate the latter property by identifying natural
properties for combinatorial auctions and showing that, for our restricted
class of players, they imply that truthful strategies are dominant. Those
properties have applicability beyond the specific auction studied.
