Distribution of surplus in sequential bargaining with endogenous recognition

I examine a sequential bargaining situation in which agents contest the right to propose an allocation. The contest can either take place at a pre-bargaining stage, yielding "persistent recognition” to propose, or recur throughout the bargaining, yielding "transitory recognition”. Equilibrium analysis reveals that surplus is distributed more unequally under persistent recognition; social cost is higher under persistent recognition if and only if it attracts a sufficient number of "active" bargainers; and individual’s incentive to propose under transitory recognition may actually increase in the number of agents, while this incentive always diminishes under persistent recognition.