Distribution of Surplus in Sequential Bargaining with Endogenous Recognition

I examine a sequential bargaining situation in which agents compete to propose by expending (unproductive) efforts. Depending on the timing of efforts, I consider two types of "recognition" to select the proposer. Whereas "persistent" recognition refers to cases where competition to propose takes place at a pre-bargaining stage as in congressional committee assignments, "transitory" recognition represents cases where competition to propose is recurring throughout the bargaining as in international negotiations and legal battles. Equilibrium analyses of two recognition types reveal that (1) surplus is distributed more unequally under persistent recognition; (2) social cost is higher under persistent recognition if and only if it attracts a sufficient number of "active" bargainers, who exert a positive effort to propose; and (3) as the number of agents increases, each agent may actually have a greater incentive to propose under transitory recognition, while this incentive is always diminished under persistent recognition.