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We study a Baron-Ferejohn (1989) type of bargaining model to which we append an investment stage. As long as no agreement is reached, a new proposer is selected randomly from the player set. A proposal is accepted if at least q players accept it. Prior to the bargaining stage, players may make investments to increase their recognition probabili- ties in the bargaining game. The investment stage is modeled in the standard way, first suggested by Tullock (1980). When investment costs are the same for all players, no symmetric stationary subgame perfect equilibria in pure investment strategies may exist if unanimity is not needed to reach an agreement. An asymmetric pure stationary equi- librium in a symmetric three-person game exists however when the discount factor is sufficiently high. An equilibrium with symmetric mixed investment strategies exists although payoff functions are not everywhere continuous with respect to investments.

We investigate a random proposer bargaining game with a dead line. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcome as the number of bargaining periods goes to infinity while the dead line is kept fixed. This limit is close to the Raiffa solution when the time horizon is very short. If the dead line goes to infinity the limit outcome converges to the time preference Nash solution. The limit outcome is given an axiomatic characterization as well.

Based on a result due to Ray and Vohra showing the possibility of inefficiency due to a coalition formation in an international emission reduction game, we consider a possibility of negotiation preceding the negotiation stage, and by means of an example, indicate that the efficiency is restored. In the equilibrium obtained, we observe a potential in which different set of coalition arises in the two stages, which could help explain what is going on in the international negotiation.