On unanimity bargaining with commitment

Abstract We study a multilateral bargaining game in which players can attempt short-lived commitments before bargaining. Existing work shows that simultaneous commitments under unanimity lead to inefficient delayed agreements due to players’ strategic over-commitments. We show that this inefficiency is not inherent in unanimity itself, but arises from a coordination failure caused by the timing of simultaneous commitments. We introduce a sequential commitment protocol: Players are randomly ordered to make their commitment attempts after observing prior stochastic commitments, modeling real-time credibility updating during negotiations. Sequential commitment yields efficient and immediate agreements in the unique stationary Markov-perfect equilibrium: The first successful committer effectively becomes the proposer, while subsequent players do not attempt to demand more than their continuation payoffs. The result is robust to heterogeneity in players’ time preferences, commitment powers, and their likelihood to be the proposer. Our findings highlight how inefficiency under unanimity arises from timing frictions—not the rule itself—and demonstrate that structured commitment can promote efficient cooperation.