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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

    as
    1. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    2. J. Alonso-Meijide & C. Bowles, 2005. "Generating Functions for Coalitional Power Indices: An Application to the IMF," Annals of Operations Research, Springer, vol. 137(1), pages 21-44, July.
    3. 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.
    4. repec:cup:apsrev:v:79:y:1985:i:03:p:673-692_22 is not listed on IDEAS
    5. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
    6. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    7. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
    8. Emilio Calvo & Esther Gutierrez, 2011. "A value for cooperative games with a coalition structure," Discussion Papers in Economic Behaviour 0311, University of Valencia, ERI-CES.
    9. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
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    Citations

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    Cited by:

    1. 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.
    2. repec:gam:jgames:v:9:y:2018:i:1:p:1-:d:124945 is not listed on IDEAS
    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. 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.

    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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