## Abstract

Classical network-formation games (NFGs) are played on directed graphs, and are used in network design and analysis. Edges in the network are associated with costs and players have reachability objectives, which they try to fulfill at a minimal cost. When several players use the same edge, they share its cost. The theoretical and practical aspects of NFGs have been extensively studied and are well understood. All studies of NFGs, however, consider an explicit representation of the network. In practice, networks are often built in a hierarchical manner. Technically, some of the vertices in the network are boxes, associated with nested sub-networks, where a sub-network may be “called” by several boxes in the network. This makes hierarchical networks exponentially more succinct than traditional “flat” networks. We introduce hierarchical network formation games (HNFGs) and study theoretical and practical aspects of the hierarchical setting. Different applications call for different cost-sharing mechanisms, which define how edge-formation costs are shared by their users. Indeed, in some applications, cost sharing should refer to the flat expansion of the network and in some it should take into account the hierarchical structure of the network. We study properties of HNFGs like stability and equilibrium inefficiency in the different mechanisms. We also study computational aspects of HNFGs, where the principal question is whether their exponential succinctness with respect to NFGs leads to an exponential increase in the complexity of reasoning about them. This question is analogous to research done in the formal-verification community about the ability to model-check hierarchical systems in their succinct presentation. We show that the picture is diverse and depends on the mechanism applied.

Original language | American English |
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Title of host publication | Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Proceedings |

Editors | Tiziana Margaria , Axel Legay |

Publisher | Springer Verlag |

Pages | 229-246 |

Number of pages | 18 |

ISBN (Print) | 9783662545768 |

DOIs | |

State | Published - 2017 |

Event | 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017 - Uppsala, Sweden Duration: 22 Apr 2017 → 29 Apr 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10205 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017 |
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Country/Territory | Sweden |

City | Uppsala |

Period | 22/04/17 → 29/04/17 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag GmbH Germany 2017.