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The essential coalitions index in games with restricted cooperation

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  • Martí Jané Ballarín

    (Universitat de Barcelona)

Abstract

We propose a new power index, which we call the essential coalitions index. Within the field of power indices, the new measure extends the Deegan-Packel power index to situations with restricted cooperation. In general, the class of games we study are not simple; with this in mind, we will introduce the essential coalitions as an analogue to the minimal winning coalitions of a simple game, since they generalize some relevant properties. We will first define the new index in terms of three reasonable assumptions, with a similar flavor to those used for the Deegan-Packel index; then, we will formally characterize the index. Finally, through numeric examples, we compare the essential coalitions index to the probabilistic Deegan-Packel index. We see that, in the latter's domain, the two indices only differ by a constant factor. Moreover, the new index is fit to analyze power in the formation of stable coalitions to run a government or a company board.

Suggested Citation

  • Martí Jané Ballarín, 2023. "The essential coalitions index in games with restricted cooperation," UB School of Economics Working Papers 2023/449, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:449web
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    File URL: http://hdl.handle.net/2445/200632
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    References listed on IDEAS

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    1. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
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    3. Pradeep Dubey, 1976. "Probabilistic Generalizations of the Shapley Value," Cowles Foundation Discussion Papers 440, Cowles Foundation for Research in Economics, Yale University.
    4. Amer, Rafel & Carreras, Francesc, 1995. "Games and Cooperation Indices," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 239-258.
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    6. Carreras, Francesc, 1991. "Restriction of simple games," Mathematical Social Sciences, Elsevier, vol. 21(3), pages 245-260, June.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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