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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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2010-01-01
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| Series: | Cubo |
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100001 |
| Summary: | 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.<br>Una de las propiedades importantes caracterizando soluciones de juegos cooperativos es con- sistencia. Esta noción establece conexiones entre los vectores solución de un juego cooperativo y aquellos de su juego reducido. Este último es obtenido a partir del juego inicial al remover uno o más jugadores y asignándoles pagos de acuerdo a un principio específico. Consistencia de una solución significa que la restricción de una solución del juego inicial a cualquier coalición, pertenece al conjunto de soluciones del correspondiente juego reducido. En este artículo, mostramos que consistencia junto con estandarización para juegos de dos personas caracterizan el valor de Banzhaf. |
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| ISSN: | 0716-7776 0719-0646 |