An important class of bargaining problems involve two negotiations who send
signals to a third party. We show that these signaling incentives signific
antly influence (1) the proposals that they offer and (2) their decisions t
o accept or reject proposals. Consider the following case: Congress makes a
take-it-or-leave-it offer (a bill) to the president, who either signs or v
etoes it. A third party is uniformed about the president's preferences; how
ever by observing the bill that Congress writes and the president's veto de
cisions, it can learn about these preferences. Since in our model the presi
dent wants to appear moderate to voters, while Congress wants him to appear
extreme, Congress sometimes writes a bill that it knows the president will
veto. Thus, despite Congress and the president being completely informed,
an uninformed third party causes the outcome to be Pareto inefficient. The
model generates many empirical predictions, and we test one of these-that t
he president's approval rating should drop after a veto.