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The Shapley value analyzed under the Felsenthal and Machover bargaining model

Author

Listed:
  • Giulia Bernardi

    (Politecnico di Milano)

  • Josep Freixas

    (Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya)

Abstract

In 1996, Felsenthal and Machover proposed a bargaining procedure for a valuable payoff in cooperative and simple games. They proved that the value underlying their bargaining scheme was the Shapley value by showing that it verifies the axioms that Shapley proposed for characterizing his value. They remarked that a direct proof of the result involves rather formidable combinatorial difficulties, but that it has some independent interest. In this paper, we prove such a combinatorial result and obtain a formula for the Shapley value that has a great potential to be extended to more general classes of games.

Suggested Citation

  • Giulia Bernardi & Josep Freixas, 2018. "The Shapley value analyzed under the Felsenthal and Machover bargaining model," Public Choice, Springer, vol. 176(3), pages 557-565, September.
    • Handle: RePEc:kap:pubcho:v:176:y:2018:i:3:d:10.1007_s11127-018-0560-2
    DOI: 10.1007/s11127-018-0560-2
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    References listed on IDEAS

    as
    1. Felsenthal, Dan S & Machover, Moshe, 1996. "Alternative Forms of the Shapley Value and the Shapley-Shubik Index," Public Choice, Springer, vol. 87(3-4), pages 315-318, June.
    2. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    3. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    4. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    5. 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.
    6. 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.
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    Cited by:

    1. Feng, Zongbao & Wu, Xianguo & Chen, Hongyu & Qin, Yawei & Zhang, Limao & Skibniewski, Miroslaw J., 2022. "An energy performance contracting parameter optimization method based on the response surface method: A case study of a metro in China," Energy, Elsevier, vol. 248(C).
    2. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    3. Kurz, Sascha & Napel, Stefan, 2018. "The roll call interpretation of the Shapley value," Economics Letters, Elsevier, vol. 173(C), pages 108-112.

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    More about this item

    Keywords

    Cooperative games; Simple games; Shapley value; Bargaining procedures; Roll-calls;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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