On stratified sampling for estimating coalitional values

Abstract

This paper addresses two sampling methodologies to respectively estimate the Owen value and the Banzhaf–Owen value for TU-games with a priori unions. Both proposals are based on stratified sampling on the set of those coalitions that are compatible with the system of unions according to their cardinalities. These sampling methodologies are analysed in terms of the theoretical properties and of the establishment of bounds for the absolute error from a statistical point of view. Finally, we evaluate the performance of these tools on several real well-known examples in the literature.