Take-it-or-leave-it offers in negotiations: Behavioral types and endogenous deadlines

This paper studies a reputational bargaining model, and investigates the effects of “exit threat” on negotiators’ equilibrium behaviors. Although it is a purely cheap talk message, exit threat is effective and has two main effects: (1) it renders the final outcome efficient and unique, and (2) shifts the bargaining power towards the negotiator who can make this threat. Setting a deadline for negotiations pressures the opponent and incentivizes her to compromise. However, a deadline that is too early makes the opponent less willing to compromise. Thus, effective deadline is uniquely determined. Last minute agreements occur with a positive probability if negotiators cannot reach an immediate agreement. Frequency of agreement has peaks at the beginning and at the end of negotiations (deadline effect), and is flat otherwise.