Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values

José M. Alonso-Meijide (), Julián Costa () and Ignacio García-Jurado ()
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José M. Alonso-Meijide: Universidade de Santiago de Compostela
Julián Costa: Universidade da Coruña
Ignacio García-Jurado: Universidade da Coruña

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 18, 1027-1035

Abstract: 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.

Keywords: Banzhaf value; Shapley value; Axiomatic characterizations; Null agent; Nullifying agent; Necessary agent; 91A12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1403-5

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