Operations-Research-Spektrum

, Volume 19, Issue 3, pp 229–234 | Cite as

On values for generalized characteristic functions

  • Estela Sanchez
  • Gustavo Bergantiños
Theoretical Papers

Abstract

In this work we study a new generalization for the Shapley value. We consider games in coalitional form in which the characteristic function is defined on all possible orders. These games are useful to model some economic situations. Different axiomatic characterizations are found for the new value using marginality, balanced contributions, the potential and the consistency property.

Key Words

Cooperative games Game-theoretic models 

Zusammenfassung

In dieser Arbeit wird eine Verallgemeinerung des Shapley-Wertes eingeführt und untersucht. Bei den zugrundeliegenden Spielen in Koalitionsform, die zur Modellierung einiger ökonomischer Sachverhalte geeignet sind, ist die charakteristische Funktion über allen Reihenfolgen der Koalitionsbildung definiert. Basierend auf den bekannten Eigenschaften des Shapley-Wertes werden verschiedene axiomatische Charakterisierungen dargestellt.

Schlüsselwörter

Kooperative Spiele Spieltheoretische Modelle 

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References

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    Hart S, Mas-Colell A (1988) The potential of the Shapley value. In: Roth A (ed) The Shapley value. Cambridge University Press, pp 126–137Google Scholar
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    Hart S, Mas-Colell A (1989) Potential, value and consistency. Econometrica 57: 589–614Google Scholar
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    Myerson R (1980) Conference structures and fair allocation rules. International Journal of Game Theory 9: 169–182Google Scholar
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    Nowak A, Radzik T (1994) The Shapley value for n-person games in generalized characteristic function form. Games and Economic Behavior 6: 150–161Google Scholar
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    Shapley L (1953) A value for n-person games. Annals of Mathematics Studies 28: 307–317Google Scholar
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    Young H-P (1985) Monotonic solutions of cooperative games. International Journal of Game Theory 14: 65–72Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Estela Sanchez
    • 1
  • Gustavo Bergantiños
    • 1
  1. 1.Faculty of EconomicsUniversity of VigoVigo, PontevedraSpain

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