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Values, Nullifiers and Dummifiers
| Content Provider | Scilit |
|---|---|
| Author | Alonso-Meijide, José María Costa, Julián García-Jurado, Ignacio |
| Copyright Year | 2019 |
| Description | 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. Book Name: Handbook of the Shapley Value |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2017-0-62091-0&isbn=9781351241410&doi=10.1201/9781351241410-5&format=pdf |
| Ending Page | 92 |
| Page Count | 18 |
| Starting Page | 75 |
| DOI | 10.1201/9781351241410-5 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2019-12-06 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Handbook of the Shapley Value Economics Axiomatic Nullifying Satisfy Banzhaf Value Dummifying Players |
| Content Type | Text |
| Resource Type | Chapter |
