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The interval Shapley value: an axiomatization

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  • S. Alparslan Gök
  • R. Branzei
  • S. Tijs

Abstract

The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real numbers. The interval Shapley value is characterized with the aid of the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. Copyright Springer-Verlag 2010

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  • S. Alparslan Gök & R. Branzei & S. Tijs, 2010. "The interval Shapley value: an axiomatization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 131-140, June.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:2:p:131-140
    DOI: 10.1007/s10100-009-0096-0
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    7. Yan-An Hwang & Wei-Yuan Yang, 2014. "A note on potential approach under interval games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 571-577, July.
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    9. Jian Li & Jian-qiang Wang & Jun-hua Hu, 2019. "Interval-valued n-person cooperative games with satisfactory degree constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1177-1194, December.
    10. Lucia Pusillo, 2013. "Banzhaf LikeValue for Games with Interval Uncertainty," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(1), pages 005-014, March.
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