Mathematical Modelling of Major League Baseball’s Final Offer Arbitration System by Carsten Berger ’19, Monday, February 11, 1 – 1:45 pm, Stetson Court Classroom 101, Mathematics Colloquium
Abstract: For decades now, Major League Baseball, as well as many other industries, has utilized Final Offer Arbitration (FOA) as a way for clubs and players to resolve salary-related disputes. Proponents of the FOA system, in which both club and player submit a salary figure and the arbitrator is bound to select exactly one of these numbers, argue it facilitates negotiated settlements. These proponents argue that in conventional arbitration, where the arbitrator is free to select any number he chooses, both sides are incentivized to submit extreme figures in belief that the arbitrator will simply split the difference between the two numbers, therefore making negotiated settlement unlikely. Under FOA, they argue, each side is incentivized to put forth a more reasonable number to increase the chances their figure is chosen.
We will start by mathematically modelling FOA and derive the Nash equilibria, and prove the Brams-Merrill theorem which states the conditions that lead to the presence of either a local or global equilibrium. We will then expand the model to encapsulate each side’s level of risk-averseness and determine its effects on the equilibrium. We will then consider the model’s implications on the efficacy of FOA as compared to conventional arbitration and conclude by examining data of the results of FOA as put in practice by Major League Baseball.