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Spectrum Value for Coalitional Games

Author

Listed:
  • Mikel Alvarez-Mozos
  • Ziv Hellman
  • Eyal Winter

Abstract

Assuming a `spectrum' or ordering on the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally asymmetric power index in which positioning along the spectrum is critical. We present both a characterisation of this value by means of properties and combinatoric formulae for calculating it. In simple majority games, the greatest power accrues to `moderate' players who are located neither at the extremes of the spectrum nor in its centre. In supermajority games, power increasingly accrues towards the extremes, and in unaninimity games all power is held by the players at the extreme of the spectrum.

Suggested Citation

  • Mikel Alvarez-Mozos & Ziv Hellman & Eyal Winter, 2012. "Spectrum Value for Coalitional Games," Discussion Paper Series dp618, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp618
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    References listed on IDEAS

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    2. Tobias Hiller, 2023. "Portfolio structures: Can they contribute to solving the low‐risk puzzle?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(7), pages 4193-4200, October.
    3. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    4. M. Josune Albizuri & Satoshi Masuya & José M. Zarzuelo, 2022. "Characterization of a value for games under restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 773-785, November.
    5. Hellman, Ziv & Peretz, Ron, 2013. "Graph value for cooperative games," LSE Research Online Documents on Economics 50073, London School of Economics and Political Science, LSE Library.
    6. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    7. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    8. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    9. Hellman, Ziv & Peretz, Ron, 2018. "Values for cooperative games over graphs and games with inadmissible coalitions," Games and Economic Behavior, Elsevier, vol. 108(C), pages 22-36.
    10. Ziv Hellman & Ron Peretz, 2015. "Values for Cooperative Games over Graphs and Games With Inadmissible Coalitions," Working Papers 2015-04, Bar-Ilan University, Department of Economics.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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