Revenue Sharing in Hierarchical Organizations: A New Interpretation of the Generalized Banzhaf Value

Abstract

This paper examines the distribution of earnings in a new model of hierarchical multi-task organizations. Each such organization is defined by a finite set of workers and tasks together with a production function that maps each allocation of workers to the tasks into an aggregate output. Tasks are ordered in degree of importance so that aggregate output increases when a worker climbs up the organization ladder. We show that the generalized Banzhaf value proposed by Freixas [1] can be used as a theory of revenue sharing in such organizations, and provide a new interpretation and formulation of this sharing rule, proving that a worker's pay is proportional to the difference between his marginal productivity at the top level and at the bottom level of the hierarchy summed over all the possible configurations of the organization. This new formulation also facilitates computation.