Alonso-Meijide, José MªCosta, JuliánGarcía-Jurado, Ignacio2025-10-232025-10-232018-09Alonso-Meijide, J.M., Costa, J. & García-Jurado, I. Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values. J Optim Theory Appl 180, 1027–1035 (2019). https://doi.org/10.1007/s10957-018-1403-50022-32391573-2878https://hdl.handle.net/2183/46083This version of the article has been accepted for publication, after peer review, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10957-018-1403-5.[Abstract]: In a cooperative game, we consider three special kinds of agents: null, nullifying, and necessary agents. A coalition with a null agent receives the same payoff if this agent leaves the coalition, a coalition with a nullifying agent receives nothing, and a coalition without a necessary agent also receives nothing. The null agent property proposes zero payoff to any null agent. We introduce new properties that propose payoffs for nullifying and necessary players. With these three properties and additivity, we obtain new characterizations of the Banzhaf and Shapley values.eng© 2018, Springer Science Business Media, LLC, part of Springer Nature. Subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms)Banzhaf valueShapley valueAxiomatic characterizationsNull agentNullifying agentNecessary agentjournal articleopen access10.1007/s10957-018-1403-5