Final-offer arbitration with a bonus

Final-offer arbitration (FOA) is an arbitration procedure, used in about a dozen states and some professional sports, under which the arbitrator is restricted to choosing one or the other of two 'final offers' proposed by two parties to a dispute. Modeled as a two-person, zero-sum game of imperfect information, in which the parties are assumed to know the probability distribution of the arbitrator's fair settlements and to make final offers to maximize their expected payoffs, FOA does not induce the two parties to converge but rather to make final offers usually two or more standard deviations apart. However, if either or both parties attach added value to winning per se (i.e., by having their offer chosen) - independent of the value of the settlement - then the Nash equilibrium final offers will tend to be drawn together and, in some cases, converge. Arbitration data from New Jersey appear to be consistent with the predictions of this model.