### Impacto

González-Arangüena, Enrique and Manuel García, Conrado Miguel and Owen, Guillermo and Pozo, M. del and Tejada Cazorla, Juan Antonio
(2004)
*Splitting graphs when calculating Myerson value for pure overhead games.*
Mathematical Methods of Operations Research, 59
(3).
pp. 479-489.
ISSN 1432-2994

PDF
Restringido a Repository staff only hasta 2020. 285kB |

Official URL: http://www.springerlink.com/content/ldf74p3lrd2pl2d9/fulltext.pdf

## Abstract

A communication situation consists of a coalitional game and a graph, the nodes of the graph corresponding to the players of the game. To calculate the Myerson value for such situations, we obtain results which extend those well known for trees and cycle-complete graphs. On the other hand, in order to reduce the associated calculus for communication situations with a pure overhead game, the possibility of splitting the graph in several subgraphs is analyzed. For each fixed decomposition of the graph, a subspace of games compatible with this decomposition is given.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Communication situations, Graph-Restricted Game, Myerson value, Pure overhead games |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15910 |

References: | Aumann R, Myerson R (1988) Endogenous formation of links between players and coalitions: an application of the Shapley value. In: Roth A (ed.) The Shapley Value. Cambridge University Press, Cambridge, United Kingdom, pp. 175–191 Borm P, Owen G, Tijs S (1992) On the position value for communication situations. SIAM Journal on Mathematics 5:305–320 Fernández JR, Algaba E, Bilbao JM, Jiménez A, Jiménez N, López JJ (2002) Generating functions for computing the Myerson value. Annals of Operations Research 109:143–158 Gómez D, González-Aranguëna E, Manuel C, Owen G, Pozo M, Tejada J (2003) Centrality in social networks: a game theoretic approach. Mathematical Social Science 46:27–54 Grofman B, Owen G (1982) A game theoretic approach to measuring centrality in social networks. Social Networks 4:213–224 Harsanyi JC (1959) A bargaining model for the cooperative n-person game. In: Tucker AW, Luce RD (eds.) Contributions of the theory of games IV, Annals of Mathematics Studies 40. Princeton University Press, Princeton, pp. 325–355 Kalay E, Samet D (1988) Weighted Shapley Values. In: Roth A (ed.) The Shapley Value.Cambridge University Press, Cambridge, pp. 83–99 Myerson RB (1977) Graphs and cooperation in games. Mathematics of Operation Research 2:225–229 Owen G (1986) Values of graph-restricted games. SIAM Journal on Algebraic and Discrete Methods 7:210–220 Shapley LS (1953) A value for n-person games. In: Kuhn H, Tucker AW (eds.) Annals of mathematics studies. Princeton University Press, Princeton, NJ, Vol. 28, pp. 307–317 Slikker M, Van den Nouweland A (2001) Social and economic networks in cooperative game theory. Kluwer Academic Publishers, Norwell, MA Van den Nouweland A (1993) Games and Graphs in Economic Situations. PhD. thesis,Tilburg University, Tilburg, The Netherlands |

Deposited On: | 11 Jul 2012 10:54 |

Last Modified: | 06 Feb 2014 10:34 |

Repository Staff Only: item control page