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Comparing Power Indices

Author

Listed:
  • CESARINO BERTINI

    (Department of Management, Economics and Quantitative Methods, University of Bergamo, via dei Caniana 2, 24127 Bergamo, Italy)

  • JOSEP FREIXAS

    (Department of Applied Mathematics III and High Engineering School, (Manresa Campus), Technical University of Catalonia, Av. de les Bases de Manresa, 71-73 Manresa, Spain)

  • GIANFRANCO GAMBARELLI

    (Department of Management, Economics and Quantitative Methods, University of Bergamo, via dei Caniana 2, 24127 Bergamo, Italy)

  • IZABELLA STACH

    (AGH University of Science and Technology, Faculty of Management, ul. Gramatyka 10, 30-067 Krakow, Poland)

Abstract

This paper aims to give a global vision concerning the state of the art of studies on 13 power indices and to establish which of them are more suitable for describing the real situations which are, from time to time, taken into consideration. In such contexts, different comparisons have been developed in terms of properties, axiomatic grounds and so on. This analysis points out various open problems.

Suggested Citation

  • Cesarino Bertini & Josep Freixas & Gianfranco Gambarelli & Izabella Stach, 2013. "Comparing Power Indices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-19.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:02:n:s0219198913400045
    DOI: 10.1142/S0219198913400045
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    References listed on IDEAS

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    1. Laruelle, Annick & Albizuri Irigoyen, Miren Iosune, 2011. "An axiomatization of success," IKERLANAK 2011-49, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. M. Albizuri & Annick Laruelle, 2013. "An axiomatization of success," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 145-155, June.
      • Albizuri Irigoyen, Miren Iosune & Laruelle, Annick, 2011. "An axiomatization of success," IKERLANAK 6256, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, March.
    4. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    5. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    6. Gianfranco Gambarelli & Guillermo Owen, 2004. "The Coming of Game Theory," Theory and Decision, Springer, vol. 56(2_2), pages 1-18, February.
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    8. Gianfranco Gambarelli & Guillermo Owen, 2004. "The Coming of Game Theory," Theory and Decision, Springer, vol. 56(1), pages 1-18, April.
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    Citations

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    Cited by:

    1. Jochen Staudacher & Felix Wagner & Jan Filipp, 2021. "Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions," Games, MDPI, vol. 13(1), pages 1-17, December.
    2. Karos, Dominik & Peters, Hans, 2018. "Effectivity and power," Games and Economic Behavior, Elsevier, vol. 108(C), pages 363-378.
    3. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    4. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    5. Izabella Stach & Jacek Mercik, 2021. "Measurement of control power in corporate networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 97-121.
    6. Izabella Stach, 2022. "Reformulation of Public Help Index θ Using Null Player Free Winning Coalitions," Group Decision and Negotiation, Springer, vol. 31(2), pages 317-334, April.
    7. 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.
    8. Somdeb Lahiri, 2021. "Pattanaik's axioms and the existence of winners preferred with probability at least half," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 109-122.
    9. Izabella Stach & Jacek Mercik, 2021. "Measurement of control power in corporate networks," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 97-121.

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    More about this item

    Keywords

    Cooperative games; power indices; simple games; voting; 91A06; 91A12; 91B12;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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