Owner-Union Compensation Game

Abstract

A firm typically consists of an owner and capital provider plus employees who together can create surplus value above individual outside opportunities. We have previously modeled such a firm as a cooperative game across these individual players with specific attention to the core and Shapley value. Here we extend the cooperative game model to include an employee union with a threshold coalition size, including the owner, for contract approval. In this model, with a binding threshold, Shapley value shades more to employees collectively, and in particular to employees with fewer outside opportunities. This seems fair, but Shapley value is not always in the core, and it can therefore be unstable relative to imputations that are shaded more to the owner and higher compensation employees. Shapley value is a standard of fairness, but it is not dominant over core imputations and it can be dominated, and therefore unstable in some cooperative game settings.