  This paper analyzes individually-rational ex post equilibrium in the VC
(Vickrey-Clarke) combinatorial auctions. If $\Sigma$ is a family of bundles of
goods, the organizer may restrict the participants by requiring them to submit
their bids only for bundles in $\Sigma$. The $\Sigma$-VC combinatorial auctions
(multi-good auctions) obtained in this way are known to be
individually-rational truth-telling mechanisms. In contrast, this paper deals
with non-restricted VC auctions, in which the buyers restrict themselves to
bids on bundles in $\Sigma$, because it is rational for them to do so. That is,
it may be that when the buyers report their valuation of the bundles in
$\Sigma$, they are in an equilibrium. We fully characterize those $\Sigma$ that
induce individually rational equilibrium in every VC auction, and we refer to
the associated equilibrium as a bundling equilibrium. The number of bundles in
$\Sigma$ represents the communication complexity of the equilibrium. A special
case of bundling equilibrium is partition-based equilibrium, in which $\Sigma$
is a field, that is, it is generated by a partition. We analyze the tradeoff
between communication complexity and economic efficiency of bundling
equilibrium, focusing in particular on partition-based equilibrium.
