An Analysis of Multivariate Final-Offer Arbitration

When negotiations fail, arbitration is often an effective means by which a binding resolution can be found. To address the many shortcomings of conventional arbitration, many industries have been using a variation called Final-Offer Arbitration since the 1970s. The mechanics are simple - rather than crafting a compromise, the judge must choose one of the two final offers proposed by the parties. Variants of the single-issue arbitration scenario, modeled as a two-player game, have been studied, but very little has been said about the game theoretic properties of the multi-issue case. In this work we define various game models for two or more issues under arbitration, study the conditions under which optimal pure strategies exist, derive these strategies, and in some cases prove that they are the unique globally optimal strategies. In particular, we look at modeling the uncertainty of arbitrator behavior with either a normal or uniform distribution, and consider a number of metrics the judge may use to make his ruling.