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Shapley's value and its axiomatization in games with prior probabilities of coalition formation

Author

Listed:
  • Kamionko, V.

    (Novosibirsk State University, Novosibirsk, Russia)

  • Marakulin, V.

    (Novosibirsk State University, Novosibirsk, Russia
    Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia)

Abstract

A new, generalized model of a cooperative game with transferable utility (TP game) is introduced and studied, in which, in addition to the characteristic function, two additional functions are used: relations between players and the probability of coalition formation, which reflect the main features of the interaction of people in specific groups. Various properties of the probability function are studied, and it is proved which of them are sufficient for its transformation into a probability measure. The generalized Shapley vector is defined for a new class of games as the mathematical expectation of a player from his marginal contribution to coalitions. Necessary and sufficient conditions are given for the generalized Shapley vector to completely coincide with the classical one introduced by Shapley himself. An axiomatization of value functions on a new class of games is proposed, which is also an extension of existing axioms in original TP games. It is proved that the (generalized) Shapley vector and only it corresponds to the introduced axioms.

Suggested Citation

  • Kamionko, V. & Marakulin, V., 2020. "Shapley's value and its axiomatization in games with prior probabilities of coalition formation," Journal of the New Economic Association, New Economic Association, vol. 46(2), pages 12-29.
    • Handle: RePEc:nea:journl:y:2020:i:46:p:12-29
    DOI: 10.31737/2221-2264-2020-46-2-1
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    References listed on IDEAS

    as
    1. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, October.
    2. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076, Elsevier.
    3. Fuad Aleskerov & Manfred Holler & Rita Kamalova, 2014. "Power distribution in the Weimar Reichstag in 1919–1933," Annals of Operations Research, Springer, vol. 215(1), pages 25-37, April.
    4. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054, Elsevier.
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    Cited by:

    1. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.

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    More about this item

    Keywords

    TU game; Shapley's value; axiomatics; probability of coalition formation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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