Hierarchical network formation games

Orna Kupferman*, Tami Tamir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations

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 languageAmerican English
Title of host publicationTools 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
EditorsTiziana Margaria , Axel Legay
PublisherSpringer Verlag
Pages229-246
Number of pages18
ISBN (Print)9783662545768
DOIs
StatePublished - 2017
Event23rd 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 201729 Apr 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10205 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd 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
Country/TerritorySweden
City Uppsala
Period22/04/1729/04/17

Bibliographical note

Publisher Copyright:
© Springer-Verlag GmbH Germany 2017.

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