  We study two-sided reputational bargaining with opportunities to issue an
ultimatum -- threats to force dispute resolution. Each player is either a
justified type, who never concedes and issues an ultimatum whenever an
opportunity arrives, or an unjustified type, who can concede, wait, or bluff
with an ultimatum. In equilibrium, the presence of ultimatum opportunities can
harm or benefit a player by decelerating or accelerating reputation building.
When only one player can issue an ultimatum, equilibrium play is unique. The
hazard rate of dispute resolution is discontinuous and piecewise monotonic in
time. As the probabilities of being justified vanish, agreement is immediate
and efficient, and if the set of justifiable demands is rich, payoffs modify
Abreu and Gul (2000), with the discount rate replaced by the ultimatum
opportunity arrival rate if the former is smaller. When both players' ultimatum
opportunities arrive sufficiently fast, there may exist multiple equilibria in
which their reputations do not build up and negotiation lasts forever.
