Characterization of the Banzhaf Value Using a Consistency Axiom
One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by giving...
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| Lenguaje: | English |
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2010
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oai:scielo:S0719-064620100001000012018-10-08Characterization of the Banzhaf Value Using a Consistency AxiomSánchez Pérez,Joss Erick Games in characteristic function form Banzhaf value consistency One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by giving them payoffs according to a specific principle. Consistency of a solution means that the restriction of a solution payoff vector of the initial game to any coalition belongs to the solution set of the corresponding reduced game. In this paper, we show that the Banzhaf value is consistent with respect to a suitable reduced game. We also show that consistency together with standardness for two-person games characterize the Banzhaf value.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.1 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100001en10.4067/S0719-06462010000100001 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Games in characteristic function form Banzhaf value consistency |
| spellingShingle |
Games in characteristic function form Banzhaf value consistency Sánchez Pérez,Joss Erick Characterization of the Banzhaf Value Using a Consistency Axiom |
| description |
One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by giving them payoffs according to a specific principle. Consistency of a solution means that the restriction of a solution payoff vector of the initial game to any coalition belongs to the solution set of the corresponding reduced game. In this paper, we show that the Banzhaf value is consistent with respect to a suitable reduced game. We also show that consistency together with standardness for two-person games characterize the Banzhaf value. |
| author |
Sánchez Pérez,Joss Erick |
| author_facet |
Sánchez Pérez,Joss Erick |
| author_sort |
Sánchez Pérez,Joss Erick |
| title |
Characterization of the Banzhaf Value Using a Consistency Axiom |
| title_short |
Characterization of the Banzhaf Value Using a Consistency Axiom |
| title_full |
Characterization of the Banzhaf Value Using a Consistency Axiom |
| title_fullStr |
Characterization of the Banzhaf Value Using a Consistency Axiom |
| title_full_unstemmed |
Characterization of the Banzhaf Value Using a Consistency Axiom |
| title_sort |
characterization of the banzhaf value using a consistency axiom |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2010 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100001 |
| work_keys_str_mv |
AT sanchezperezjosserick characterizationofthebanzhafvalueusingaconsistencyaxiom |
| _version_ |
1714206761619030016 |