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The value of a player in n-person games

Author

Listed:
  • Kjell Hausken

    (School of Economics, Culture and Social Sciences, University of Stavanger, P.O. Box 2557 Ullandhaug, N-4091 Stavanger, Norway)

  • Matthias Mohr

    (Deutsche Bundesbank, Economics Department, Wilhelm-Epstein-Strasse 14-16, P.O. Box 100602, D-60006 Frankfurt am Main, Germany)

Abstract

The article decomposes the Shapley value into a value matrix which gives the value of every player to every other player in n-person games. Element ij(v) in the value matrix is positive, zero, or negative, dependent on whether row player i is beneficial, has no impact, or is not beneficial for column player j. The elements in each row and in each column of the value matrix sum up to the Shapley value of the respective player. The value matrix is illustrated by the voting procedure in the European Council of Ministers 1981-1995.

Suggested Citation

  • Kjell Hausken & Matthias Mohr, 2001. "The value of a player in n-person games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 465-483.
    • Handle: RePEc:spr:sochwe:v:18:y:2001:i:3:p:465-483
    Note: Received: 9 September 1998/Accepted: 11 February 2000
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    References listed on IDEAS

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    1. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    Cited by:

    1. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "Three-valued simple games," Theory and Decision, Springer, vol. 85(2), pages 201-224, August.
    2. Bernd Irlenbusch & Matthias Sutter, 2006. "An experimental analysis of voting in the Stability and Growth Pact in the European Monetary Union," Public Choice, Springer, vol. 129(3), pages 417-434, December.
    3. Kjell Hausken, 2020. "The Shapley value of coalitions to other coalitions," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-10, December.
    4. Julien Reynaud & Fabien Lange & Łukasz Gątarek & Christian Thimann, 2011. "Proximity in Coalition Building," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(3), pages 111-132, September.
    5. Alessio Guandalini & Claudio Ceccarelli, 2022. "Impact measurement and dimension reduction of auxiliary variables in calibration estimator using the Shapley decomposition," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 759-784, October.
    6. Filipe Bandeiras & Álvaro Gomes & Mário Gomes & Paulo Coelho, 2023. "Application and Challenges of Coalitional Game Theory in Power Systems for Sustainable Energy Trading Communities," Energies, MDPI, vol. 16(24), pages 1-42, December.
    7. Tobias Hiller, 2023. "Measuring the Difficulties in Forming a Coalition Government," Games, MDPI, vol. 14(2), pages 1-15, March.

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