Reputational bargaining and deadlines

How will agents behave when bargaining in the face of an upcoming deadline? If irrational types exist, committed to their bargaining positions, rational agents will imitate this tough behavior to gain reputational benefits, even though this may result in the deadline being missed. Notably, if agents are patient and irrational types are committed to fixed demands then agreement must necessarily follow a U shape: deals are made either at time zero, or arbitrarily close to the deadline, with a positive fraction of rational agents failing to agree. But what demands will rational agents make? The model gives clear answers when the the probability of commitment is small. Maintaining the fixed demand assumption for irrational types, rational agents should ask for half the available surplus regardless of their relative discount rates, guaranteeing this payoff as the behavioral perturbation vanishes. If irrational types can commit to time varying demands, however, then rational agents should imitate a generalized Rubinstein (alternating offers) demand to secure the associated time zero payoff in the limit. The link between reputational and alternating offer models is driven by the properties of symmetry and a respect for backward induction, common to both. In addition to insights into the mechanics of reputational bargaining, the findings also raise questions about the correct assumptions to make about types and the motivation of their commitment.