Equilibrium Strategies for Final-Offer Arbitration: There is no Median Convergence

Final-offer arbitration is a procedure for settling disputes between two parties in which an arbitrator chooses the final offer of the party closest to what he considers a fair settlement. This procedure is 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 bids in an infinite strategy space that maximize their expected payoffs. Necessary and sufficient conditions for there to be local and global equilibria in pure strategies are derived, and necessary conditions for mixed strategies in a particular case are found. Such equilibria, when they exist in pure strategies, represent bids which are symmetric about the median and, for most common distributions, are separated from one another by two or more standard deviations. This finding suggests that final-offer arbitration may not accomplish its avowed purpose of inducing the two parties to converge on what they perceive to be the arbitrator's median fair settlement.