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**On the structure of the core of balanced games.**
*(English)*
Zbl 1265.91016

Summary: The uniform competitive solutions (u.c.s.) are basically stable sets of proposals involving several coalitions which are not necessarily disjoint. In the general framework of NTU games, the uniform competitive solutions have been defined in the author’s two earlier papers [Kybernetika 32, No. 5, 483–490 (1996; Zbl 1042.91509); Stud. Econ. Theory 8, 475–489 (1999; Zbl 0977.91005)]. The general existence results cover most situations formalized in the framework of cooperative game theory, including those for which the coalitional function is allowed to have empty values. The present approach concerns the situation where the coalition configurations are balanced. One shows that if the coalitional function has nonempty values, the game admits balanced u.c.s. To each u.c.s. one associates an “ideal payoff vector” representing the utilities that the coalitions promise to the players. One proves that if the game is balanced then the core and the strong core consist of the ideal payoff vectors associated to all balanced u.c.s.

### MSC:

91A12 | Cooperative games |

### References:

[1] | Aliprantis C. D., Brown D. J., Burkinshaw O.: Existence and Optimality of Competitive Equilibria. Springer-Verlag, Berlin 1990 · Zbl 0676.90001 |

[2] | Bennett E., Zame W. R.: Bargaining in cooperative games. Internat. J. Game Theory 17 (1988), 279-300 · Zbl 0661.90107 |

[3] | Ichiishi T.: Game Theory for Economic Analysis. Academic Press, New York 1983 · Zbl 0522.90104 |

[4] | McKelvey R. D., Ordeshook P. C., Winer M. D.: Competitive solution for \(N\)-person games without transferable utility, with an application to committee games. The American Political Science Review 72 (1978), 599-615 |

[5] | Stefanescu A.: Coalitional stability and rationality in cooperative games. Kybernetika 32 (1996), 483-490 · Zbl 1042.91509 |

[6] | Stefanescu A.: Predicting proposal configurations in cooperative games and exchange economies. Current Trends in Economics (A. Alkan, C. D. Aliprantis and N. C. Yannelis, Springer Verlag, Berlin 1999, pp. 475-489 · Zbl 0977.91005 |

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