Reputational Bargaining Under Knowledge of Rationality

Two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus. The share of the surplus that a player can guarantee herself under first-order knowledge of rationality is determined (as a function of her probability of becoming committed), as is the bargaining posture that she must announce in order to guarantee herself this much. This “maxmin” share of the surplus is large relative to the probability of becoming committed (e.g., it equals 30% if the commitment probability is 1 in 10, and equals 7% if the commitment probability is 1 in 1 million), and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement. I also consider whether a larger share can be guaranteed if there is higher-order knowledge of rationality, and relate the outcome of the model to the outcomes of a broad class of discrete-time bargaining procedures with frequent offers.