Proposal Power and Majority Rule in Multilateral Bargaining with Costly Recognition

This paper studies a sequential bargaining model in which, as in the rent-seeking literature, agents expend resources to be the proposer, and agreement requires affirmative votes of either all agents or a subset of them. By focusing on the Stationary Subgame Perfect Equilibrium, it is found that (1) under the unanimity voting rule, all agents expend the same amount of resources, regardless of their time preferences. (2) Under a nonunanimity rule however, more patient agents expend greater resources, and are thus more likely to propose. Yet, they can end up with a lower payoff than less patient agents. (3) While, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule. (4) Bargaining as a coalition pays off only if the coalition is large enough. (5) When the surplus is endogenous to the group, groups that require more consensus in their distribution are more likely to expand; and (6) when bargaining delays are possible, costly recognition induces agents to reach an agreement too soon from the social standpoint, even under the unanimity rule..