This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.