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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 with�a 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.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 680.

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Date of creation: 28 Oct 2013
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Handle: RePEc:oxf:wpaper:680

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Keywords: Apex Games; Core Stability; Hedonic Games; Strong monotony;

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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, 2005. "Government versus opposition: Who should be who in the 16th German Bundestag?," Working Papers 375, Bielefeld University, Center for Mathematical Economics.
  3. Dinko Dimitrov & Claus-Jochen Haake, 2006. "A note on the paradox of smaller coalitions," Working Papers 386, Bielefeld University, Center for Mathematical Economics.
  4. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  5. Dimitrov, Dinko & Haake, Claus-Jochen, 2008. "Stable governments and the semistrict core," Games and Economic Behavior, Elsevier, vol. 62(2), pages 460-475, March.
  6. Sagonti, Emanuela, 1991. "On the Strong Monotonicity of Power Indices," International Journal of Game Theory, Springer, vol. 20(1), pages 13-22.
  7. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  8. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  9. Iehlé, Vincent, 2007. "The Core-Partition of Hedonic Games," Economics Papers from University Paris Dauphine 123456789/87, Paris Dauphine University.
  10. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
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