  We revisit the connection between bargaining and equilibrium in exchange
economies, and study its algorithmic implications. We consider bargaining
outcomes to be allocations that cannot be blocked (i.e., profitably re-traded)
by coalitions of small size and show that these allocations must be approximate
Walrasian equilibria. Our results imply that deciding whether an allocation is
approximately Walrasian can be done in polynomial time, even in economies for
which finding an equilibrium is known to be computationally hard.
