# Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness

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## Abstract

The objective of this paper is to study stable coalition structures in symmetric majority games. We assume that players deviate from a coalition structure to another to maximize their power given by the Owen power index. We introduce three myopic core concepts and one farsighted stability concept, the farsighted vNM stable set. Our main result is that the pessimistic core, the largest myopic core, coincides with some farsighted vNM stable set for any number of players. Moreover, we show that a coalition structure belongs to the pessimistic core and the farsighted vNM stable set if and only if it contains an exact majority coalition.

## Keywords

Myopia Farsightedness Coalition structure Symmetric majority game## References

- Abe, T. (2017). Consistency and the core in games with externalities.
*International Journal of Game Theory*. https://doi.org/10.1007/s00182-017-0581-y CrossRefGoogle Scholar - Abe, T., & Funaki, Y. (2017). The non-emptiness of the core of a partition function form game.
*International Journal of Game Theory*,*46*, 715–736.CrossRefGoogle Scholar - Aumann, R. J., & Drèze, J. H. (1974). Cooperative games with coalition structures.
*International Journal of game theory*,*3*, 217–237.CrossRefGoogle Scholar - Alonso-Meijide, J. M., Bowles, C., Holler, M. J., & Napel, S. (2009). Monotonicity of power in games with a priori unions.
*Theory and Decision*,*66*, 17–37.CrossRefGoogle Scholar - Banerjee, S., Konishi, H., & Sönmez, T. (2001). Core in a simple coalition formation game.
*Social Choice and Welfare*,*18*, 135–153.CrossRefGoogle Scholar - Bloch, F. (1996). Sequential formation of coalitions in games with externalities and fixed payoff division.
*Games and Economic Behavior*,*14*, 90–123.CrossRefGoogle Scholar - Bogomolnaia, A., & Jackson, M. O. (2002). The stability of hedonic coalition structures.
*Games and Economic Behavior*,*38*, 201–230.CrossRefGoogle Scholar - Casajus, A. (2009). Outside options, component efficiency, and stability.
*Games and Economic Behavior*,*65*, 49–61.CrossRefGoogle Scholar - Chwe, M. S. Y. (1994). Farsighted coalitional stability.
*Journal of Economic Theory*,*63*, 299–325.CrossRefGoogle Scholar - Diamantoudi, E., & Xue, L. (2003). Farsighted stability in hedonic games.
*Social Choice and Welfare*,*21*, 39–61.CrossRefGoogle Scholar - Diamantoudi, E., & Xue, L. (2007). Coalitions, agreements and efficiency.
*Journal of Economic Theory*,*136*, 105–125.CrossRefGoogle Scholar - Funaki, Y., & Yamato, T. (1999). The core of an economy with a common pool resource: A partition function form approach.
*International Journal of Game Theory*,*28*, 157–171.CrossRefGoogle Scholar - Greenberg, J. (1994).
*Coalition structures. Handbook of game theory with economic applications, chapter 37*. Amsterdam: Elsevier.Google Scholar - Harsanyi, J. C. (1974). An equilibrium-point interpretation of stable sets and a proposed alternative definition.
*Management Science*,*20*, 1472–1495.CrossRefGoogle Scholar - Hart, S., & Kurz, M. (1983). Endogenous formation of coalitions.
*Econometrica*,*51*, 1047–1064.CrossRefGoogle Scholar - Hart, S., & Kurz, M. (1984). Stable coalition structures. In M. J. Holler (Ed.),
*Coalitions and collective action*(Vol. 51, pp. 235–258). Wüerzburg: Physica-Verlag.Google Scholar - Kamijo, Y. (2009). A two-step Shapley value for cooperative games with coalition structures.
*International Game Theory Review*,*11*, 207–214.CrossRefGoogle Scholar - Kóczy, L. (2007). A recursive core for partition function form games.
*Theory and Decision*,*63*, 41–51.CrossRefGoogle Scholar - Kóczy, L., & Lauwers, L. (2004). The coalition structure core is accessible.
*Games and Economic Behavior*,*48*, 86–93.CrossRefGoogle Scholar - Mauleon, A., & Vannetelbosch, V. (2004). Farsightedness and cautiousness in coalition formation games with positive spillovers.
*Theory and Decision*,*56*, 291–324.CrossRefGoogle Scholar - Owen, G. (1977). Values of games with a priori unions. In
*Essays in mathematical economics and game theory*(pp. 76–88). Berlin: Springer.Google Scholar - Ray, D., & Vohra, R. (1997). Equilibrium binding agreements.
*Journal of Economic Theory*,*73*, 30–78.CrossRefGoogle Scholar - Ray, D., & Vohra, R. (2015). The farsighted stable set.
*Econometrica*,*83*, 977–1011.CrossRefGoogle Scholar - Wiese, H. (2007). Measuring the power of parties within government coalitions.
*International Game Theory Review*,*9*, 307–322.CrossRefGoogle Scholar - Xue, L. (1997). Nonemptiness of the largest consistent set.
*Journal of Economic Theory*,*73*, 453–459.CrossRefGoogle Scholar

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