Optimal value commitment in bilateral bargaining

Abstract

We study the role of commitment as a source of strategic power in a non-cooperative bargaining game. Two impatient players bargain about the division of a shrinking surplus under a standard bargaining protocol in discrete time with constant recognition probabilities. Before bargaining, a player can commit to some part of the surplus. This commitment remains binding until the surplus has shrunk below the amount that the player is committed to. Intuitively, one cannot remain committed to something which has become impossible. The model offers insight on the relative importance of proposal power and commitment for the bargaining outcome. In a version of the game where both players may simultaneously choose their commitments, the equal split emerges from within a range of equilibrium divisions as a focal point which is robust to changes in the model parameters.