We study a bargaining model with a disagreement game between offers and counteroffers. In order to characterize the set of its subgame perfect equilibrium payoffs, we provide a recursive technique that relies on the Pareto frontier of equilibrium payoffs. When players have different time preferences, reaching an immediate agreement may not be Pareto efficient. The recursive technique developed in this paper generalizes that of Shaked and Sutton (1984) by incorporating the possibility of making unacceptable proposals into the backward induction analysis. Results from this paper extend all the previous findings and resolve some open issues in the current literature.
Bargaining negotiation time preference endogenous threats