Commitment in Alternating Offers Bargaining

We extend the Ståhl-Rubinstein alternating-offer bargaining procedure to allow players, prior to each bargaining round, to simultaneously and visibly commit to some share of the pie. If commitment costs are small but increasing in the committed share, then the unique outcome consistent with common belief in future rationality (Perea, 2010), or more restrictively subgame perfect Nash equilibrium, exhibits a second mover advantage. In particular, as the smallest share of the pie approaches zero, the horizon approaches infinity, and commitment costs approach zero, the unique bargaining outcome corresponds to the reversed Rubinstein outcome (d =(1 + d); 1=(1 + d)), where d is the common discount factor.

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