  We define a model of interactive communication where two agents with private
types can exchange information before a game is played. The model contains
Bayesian persuasion as a special case of a one-round communication protocol. We
define message complexity corresponding to the minimum number of interactive
rounds necessary to achieve the best possible outcome. Our main result is that
for bilateral trade, agents don't stop talking until they reach an efficient
outcome: Either agents achieve an efficient allocation in finitely many rounds
of communication; or the optimal communication protocol has infinite number of
rounds. We show an important class of bilateral trade settings where efficient
allocation is achievable with a small number of rounds of communication.
