Commitment in alternating offers bargaining

We extend the Stahl-Rubinstein alternating-offer bargaining procedure to allow players to simultaneously and visibly commit to some share of the pie prior to, and for the duration of, each bargaining round. If commitment costs are small but increasing in the committed share, then the unique subgame perfect equilibrium outcome exhibits a second mover advantage. In particular, as the horizon approaches infinity, and commitment costs approach zero, the unique bargaining outcome corresponds to the reversed Rubinstein outcome (delta(1 + delta), 1/(1 + delta)), where 3 is the common discount factor