Bargaining and Rent Seeking

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.