Publication: Splitting graphs when calculating Myerson value for pure overhead games
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Publication Date
2004-07
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Springer
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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.
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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