RT Journal Article T1 Splitting graphs when calculating Myerson value for pure overhead games A1 González-Arangüena, Enrique A1 Manuel García, Conrado Miguel A1 Owen, Guillermo A1 Pozo, M. del A1 Tejada Cazorla, Juan Antonio AB 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. PB Springer SN 1432-2994 YR 2004 FD 2004-07 LK https://hdl.handle.net/20.500.14352/50046 UL https://hdl.handle.net/20.500.14352/50046 LA eng NO 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. 175–191Borm P, Owen G, Tijs S (1992) On the position value for communication situations. SIAM Journal on Mathematics 5:305–320Fernández JR, Algaba E, Bilbao JM, Jiménez A, Jiménez N, López JJ (2002) Generating functions for computing the Myerson value. Annals of Operations Research 109:143–158Gómez D, González-Aranguëna E, Manuel C, Owen G, Pozo M, Tejada J (2003) Centrality in social networks: a game theoretic approach. Mathematical Social Science 46:27–54Grofman B, Owen G (1982) A game theoretic approach to measuring centrality in social networks. Social Networks 4:213–224Harsanyi 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. 325–355Kalay E, Samet D (1988) Weighted Shapley Values. In: Roth A (ed.) The Shapley Value.Cambridge University Press, Cambridge, pp. 83–99Myerson RB (1977) Graphs and cooperation in games. Mathematics of Operation Research 2:225–229Owen G (1986) Values of graph-restricted games. SIAM Journal on Algebraic and Discrete Methods 7:210–220Shapley 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. 307–317Slikker M, Van den Nouweland A (2001) Social and economic networks in cooperative game theory. Kluwer Academic Publishers, Norwell, MAVan den Nouweland A (1993) Games and Graphs in Economic Situations. PhD. thesis,Tilburg University, Tilburg, The Netherlands DS Docta Complutense RD 2 may 2024