Alonso-Meijide, José MªCosta, JuliánGarcía-Jurado, Ignacio2025-10-232025-10-232019Alonso-Meijide, J. M., Costa, J., & García-Jurado, I. (2019). Values, nullifiers and dummifiers. In Handbook of the Shapley value (pp. 75-92). Chapman and Hall/CRC. ISBN: 978-0-8153-7468-8.97808153746889781351241410https://hdl.handle.net/2183/46085This is an Accepted Manuscript version of the following paper: Alonso-Meijide, J. M., Costa, J., & García-Jurado, I. (2019). ‘Values, nullifiers and dummifiers’ , accepted for publication in Handbook of the Shapley value (pp. 75-92). Chapman and Hall/CRC. ISBN: 978-0-8153-7468-8. https://doi.org/10.1201/9781351241410 .[Abstract]: In this chapter, we provide new axiomatic characterizations of the Shapley and Banzhaf values using properties concerning nullifying and dummifying players. Then, we introduce a novel value for TU-games using an axiomatic approach: the e-Banzhaf value. Specifically, we take the properties of efficiency, symmetry, additivity, and combine them with the property for nullifying players that we consider most natural: the nullifying players pay for the mean property. We prove that these four properties characterize the e-Banzhaf value. This novel value possesses some properties of the Shapley value and some of the Banzhaf value, and can be seen as a kind of efficient variation of the Banzhaf value. However, it is not invariant to S-equivalence and it does not satisfy the dummifying players pay for the mean property. Finally, we introduce an alternative novel value for TU-games: the ie-Banzhaf value. It is the unique value for TU-games that satisfies efficiency, symmetry, additivity and the dummifying players pay for the mean property. We prove that the ie-Banzhaf value is also a kind of efficient variation of the Banzhaf value and that it is invariant to S-equivalence.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Nullifying playerBanzhaf valueCooperative gameDummifying playerbook partopen access10.1201/9781351241410