### Abstract

A two-level hierarchical game of n + 1 persons Г with coalitional partition is considered. The control center is on the first level of the hierarchy, and the n players are on the second level. The players on the second level are formed coalitions. An algorithm for solving of this game is described. According to this algorithm PMS-vector, first introduced by Petrosyan L. A. and Mamkina S. I., or generalized PMS-vector in mixed strategies in a coalitional game between players from the lower level of the hierarchical game is found on the first step. Then game Г can be considered as a two-level hierarchical Stackelberg game of two persons, where control center is on the first level of the hierarchy and player with strategies which are Nash equilibrium situations from coalitional game of first step algorithm. Then it is possible to find the Stackelberg strategy for the center on the second step algorithm. The existence of solution for suggested algorithm is proved. The algorithm is illustrated by a two-level hiera

Original language | English |
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Title of host publication | SOLUTIONS FOR N + 1 PERSON HIERARCHICAL STACKELBERG GAMES WITH COALITIONAL PARTITIONS |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 240-243 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

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## Cite this

Grigor'eva, X. V. (2015). SOLUTIONS FOR N + 1 PERSON HIERARCHICAL STACKELBERG GAMES WITH COALITIONAL PARTITIONS. In

*SOLUTIONS FOR N + 1 PERSON HIERARCHICAL STACKELBERG GAMES WITH COALITIONAL PARTITIONS*(pp. 240-243). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/DOI: 10.1109/SCP.2015.7342115