  We discuss bundle auctions within the framework of an integer allocation
problem. We show that for multi-unit auctions, of which bundle auctions are a
special case, market equilibrium and constrained market equilibrium are
equivalent concepts. This equivalence, allows us to obtain a computable
necessary and sufficient condition for the existence of constrained market
equilibrium for bundle auctions. We use this result to obtain a necessary and
sufficient condition for the existence of market equilibrium for multi-unit
auctions. After obtaining the induced bundle auction of a nonnegative TU game,
we show that the existence of market equilibrium implies the existence of a
possibly different market equilibrium as well, which corresponds very naturally
to an outcome in the matching core of the TU game. Consequently we show that
the matching core of the nonnegative TU game is non-empty if and only if the
induced market game has a market equilibrium.
