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Coalition Formation in General Apex Games

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  • Dominik Karos

Abstract

We generalize the class of apex game by combining a winning coalition of symmetric minor players witha collection of apex sets which can form winning coalitions only together with a fixed quota of minor players. By applying power indices to these games and their subgames we generate players' preferences over coalitions which we use to define a coalition formation game. We focus on strongly monotonic power indices and investigate under which conditions on the initial general apex game there are core stable coalitions in the resulting coalition formation game. Besides several general results, we develop condition for the Shapley-Shubik index, the Banzhaf index, and the normalized Banzhaf index in particular. It turns out that many statements can be easily verified for arbitrary collections of apex sets. Nevertheless, we give some relations between the collection of apex sets and the set of core stable coalitions.

Suggested Citation

  • Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:680
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    References listed on IDEAS

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    1. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    2. Dinko Dimitrov & Claus-Jochen Haake, 2008. "A note on the paradox of smaller coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 571-579, May.
    3. Dinko Dimitrov & Claus-Jochen Haake, 2006. "Government versus Opposition: Who Should be Who in the 16th German Bundestag?," Journal of Economics, Springer, vol. 89(2), pages 115-128, November.
    4. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    7. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    8. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    9. Sagonti, Emanuela, 1991. "On the Strong Monotonicity of Power Indices," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 13-22.
    10. repec:dau:papers:123456789/87 is not listed on IDEAS
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    Cited by:

    1. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.
    2. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Apex Games; Core Stability; Hedonic Games; Strong monotony;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G34 - Financial Economics - - Corporate Finance and Governance - - - Mergers; Acquisitions; Restructuring; Corporate Governance

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