  We study markets of indivisible items in which price-based (Walrasian)
equilibria often do not exist due to the discrete non-convex setting. Instead
we consider Nash equilibria of the market viewed as a game, where players bid
for items, and where the highest bidder on an item wins it and pays his bid. We
first observe that pure Nash-equilibria of this game excatly correspond to
price-based equilibiria (and thus need not exist), but that mixed-Nash
equilibria always do exist, and we analyze their structure in several simple
cases where no price-based equilibrium exists. We also undertake an analysis of
the welfare properties of these equilibria showing that while pure equilibria
are always perfectly efficient ("first welfare theorem"), mixed equilibria need
not be, and we provide upper and lower bounds on their amount of inefficiency.
