Reputational bargaining and deadlines

I introduce irrational types, who are committed to their demands, into a bargaining model with an uncertain deadline for agreement. Rational agents imitate these demands, hoping to benefit from a “tough” reputation. When irrational types are committed to fixed demands and agents are patient, this provides an explanation for “deadline effects” in bargaining: agreement is “U-shaped”, occurring either immediately or arbitrarily close to the deadline, and some rational agents fail to agree. I also identify agents’ optimal demands when the prior probability of irrationality is small. Maintaining the assumption of types committed to fixed demands, a rational agent should imitate a type that demands half the surplus, regardless of her impatience, to guarantee this payoff as the behavioral perturbation vanishes. If irrational types can commit to time-varying demands, however, then a rational agent should imitate a generalized Rubinstein demand type to secure the associated time zero payoff in the limit. This generalized Rubinstein demand is the limit solution to an alternating offers game in the deadline environment, as the time between offers becomes small; it is a timevarying convex combination of the infinite horizon (no deadline) Rubinstein demand and a half, which converges to a half when the deadline is imminent.