A seller of a divisible good faces several identical buyers. The
quality of the good may be low or high, and is the seller's
private information. The seller has strictly convex preferences
that satisfy a single-crossing property. Buyers compete by posting
menus of nonexclusive contracts, so that the seller can
simultaneously and privately trade with several buyers. We provide
a necessary and sufficient condition for the existence of a
pure-strategy equilibrium. Aggregate equilibrium trades are
unique. Any traded contract must yield zero profit. If a quality
is actually traded, then it is efficiently traded. Depending on
parameters, both qualities may be traded, or only one of them, or
the market may break down to a no-trade equilibrium.