Perfect Equilibria in a Negotiation Model with Different Time Preferences

There has been a long debate on equilibrium characterization in the negotiation model when players have different time preferences. We show that players behave quite differently under different time preferences than under common time preferences. Conventional analysis in this literature relies on the key assumption that all continuation payoffs are bounded from above by the bargaining frontier. However, when players have different time preferences, intertemporal trade may lead to continuation payoffs above the bargaining frontier. We provide a thorough study of this problem without imposing the conventional assumption. Our results tie up all the previous findings, and also clarify the controversies that arose in the past.