Saavedra Nieves, Alejandro2023-01-242023-01-242023Saavedra-Nieves, A. On stratified sampling for estimating coalitional values. Ann Oper Res 320, 325–353 (2023). https://doi.org/10.1007/s10479-022-05044-00254-5330http://hdl.handle.net/10347/29997This 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 literatureeng© 2023 The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Multi-agent systemsGames with a priori unionsCoalitional valuesSamplingjournal articles10479-022-05044-01572-9338open access