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Coalition formation in general apex games under monotonic power indices

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  • Karos, Dominik

Abstract

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.

Suggested Citation

  • Karos, Dominik, 2014. "Coalition formation in general apex games under monotonic power indices," Games and Economic Behavior, Elsevier, vol. 87(C), pages 239-252.
    • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:239-252
    DOI: 10.1016/j.geb.2014.05.011
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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. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    5. 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.
    6. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    7. repec:dau:papers:123456789/87 is not listed on IDEAS
    8. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    9. Dimitrov, Dinko & Haake, Claus-Jochen, 2008. "Stable governments and the semistrict core," Games and Economic Behavior, Elsevier, vol. 62(2), pages 460-475, March.
    10. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    11. 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.
    12. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.
    2. Dominik Karos, 2016. "Stable partitions for games with non-transferable utility and externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 817-838, November.
    3. Takaaki Abe, 2022. "Stable coalition structures and power indices for majority voting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1413-1432, December.
    4. Dominik Karos, 2016. "A note on monotonic power indices, smaller coalitions, and new members," Theory and Decision, Springer, vol. 81(1), pages 89-100, June.
    5. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.

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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
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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