  We investigate the allocation of a co-owned company to a single owner using
the Texas Shoot-Out mechanism with private valuations. We identify Knightian
Uncertainty about the peer's distribution as a reason for its deterrent effect
of a premature dissolving. Modeling uncertainty by a distribution band around a
reference distribution $F$, we derive the optimal price announcement for an
ambiguity averse divider. The divider hedges against uncertainty for valuations
close to the median of $F$, while extracting expected surplus for high and low
valuations. The outcome of the mechanism is efficient for valuations around the
median. A risk neutral co-owner prefers to be the chooser, even strictly so for
any valuation under low levels of uncertainty and for extreme valuations under
high levels of uncertainty. If valuations are believed to be close, less
uncertainty is required for the mechanism to always be efficient and reduce
premature dissolvements.
