Abstract
A well-known theorem due to Keane (1969) states that for a finite cooperative game, the Shapley vector is the solution of a minimization problem for a certain quadratic functional. For cooperative games with a countable number of players we introduce an analogue of Keane’s functional and define the Shapley value as the solution of the corresponding minimization problem. It is shown that this definition is consistent, and the solution is unique.
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References
Aumann, R.J., and L.S. Shapley (1976): Values of non-atomic games. Princeton, Princeton University Press.
Keane, M. (1969): Some topics in N-person game theory. Thesis, Northwestern University, Evanston, Illiois.
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© 2006 Springer-Verlag Berlin Heidelberg
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Diubin, G. (2006). On the Shapley function for games with an infinite number of players. In: Driessen, T.S.H., van der Laan, G., Vasil’ev, V.A., Yanovskaya, E.B. (eds) Russian Contributions to Game Theory and Equilibrium Theory. Theory and Decision Library C:, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32061-X_6
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DOI: https://doi.org/10.1007/3-540-32061-X_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31405-9
Online ISBN: 978-3-540-32061-6
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