  Bilateral trade is one of the most natural and important forms of economic
interaction: A seller has a single, indivisible item for sale, and a buyer is
potentially interested. The two parties typically have different, privately
known valuations for the item, and ideally, they would like to trade if the
buyer values the item more than the seller. The celebrated impossibility result
by Myerson and Satterthwaite shows that any mechanism for this setting must
violate at least one important desideratum. In this paper, we investigate a
richer paradigm of bilateral trade, with many self-interested buyers and
sellers on both sides of a single trade who cannot be excluded from the trade.
We show that this allows for more positive results. In fact, we establish a
dichotomy in the possibility of trading efficiently. If in expectation, the
buyers value the item more, we can achieve efficiency in the limit. If this is
not the case, then efficiency cannot be achieved in general. En route, we
characterize trading mechanisms that encourage truth-telling, which may be of
independent interest. We also evaluate our trading mechanisms experimentally,
and the experiments align with our theoretical results.
