Abstract
We reconsider the Myerson value and the position value for communication situations. In case the underlying game is a unanimity game, we show that each of these values can be computed using the inclusion— exclusion principle. Linearity of both values permits us to calculate them without needing the dividends of the induced games (graph-restricted game and link game). The expression of these dividends is only derived in the existing literature for special communication situations. Moreover, the associated inclusion—exclusion decomposability property depends on what we have called the graph allocation rule. This rule is the relative degree (relative indicator) for the position value (Myerson value).
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References
Borm, P., Owen, G. and Tijs, S. (1992), ‘On the position value for communication situations, SIAM Journal on Discrete Mathematics 5, 305–320.
Gómez, D., Gonzalez-Arangiiena, E., Manuel, C., Owen, G., Pozo, M. and Tejada, J. (2003), Centrality and Power in social networks: A game theoretic approach, Mathematical Social Science 46, 27–54.
Meessen, R. (1988), Communication Games, Master’s Thesis, Department of Mathematics, University of Nijmegen, The Netherlands (in Dutch).
Myerson, R. (1977), Graph and cooperation in games, Mathematics of Operations Research 2, 225–229.
Owen, G. (1986), Values of Graph-restricted games, SIAM Journal on Algebraic and Discrete Methods 7, 210–220.
Shapley, L.S. (1953), A value for n-person games, in A.W. Tucker and H. Kuhn (eds), Annals of Mathematics Studies, Princeton, NJ: Princeton University Press, 307–317.
Slikker, M. (2003), A characterization of the position value, Beta working paper WP-96, Eindhoven, Technische Universiteit Eindhoven, The Netherlands.
Slikker, M. and Van den Nouweland, A. (2001), Social and Economic Networks in Cooperative Game Theory, Boston: Kluwer Academic Publishers.
Van den Nouweland, A. (1993), Games and Graphs in Economic Situations, Ph.D. Thesis, Tilburg University, Tilburg, The Netherlands.
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© 2004 Springer Science+Business Media New York
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Gómez, D., González-Arangüena, E., Manuel, C., Owen, G., del Pozo, M. (2004). A Unified Approach to the Myerson Value and the Position Value. In: Gambarelli, G. (eds) Essays in Cooperative Games. Theory and Decision Library, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-2936-3_6
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DOI: https://doi.org/10.1007/978-1-4020-2936-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5260-8
Online ISBN: 978-1-4020-2936-3
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