Vitality Indices are Equivalent to Induced Game-Theoretic Centralities

Skibski, Oskar

doi:10.24963/ijcai.2021/56

Vitality Indices are Equivalent to Induced Game-Theoretic Centralities

Oskar Skibski

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Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence. Main Track. Pages 398-404.

https://doi.org/10.24963/ijcai.2021/56

Keywords

Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems
Agent-based and Multi-agent Systems: Cooperative Games
Machine Learning Applications: Networks

Abstract

Vitality indices form a class of centrality measures that assess the importance of a node based on the impact its removal has on the network. To date, theoretical analysis of this class is lacking. In this paper, we show that vitality indices can be characterized using the axiom of Balanced Contributions proposed by Myerson in the coalitional game theory literature. We explore the link between both fields and show an equivalence between vitality indices and induced game theoretic centralities based on the Shapley value. Our characterization allows us to easily determine which known centrality measures are vitality indices.

Oskar Skibski. 2021. Vitality Indices are Equivalent to Induced Game-Theoretic Centralities. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI-21. IJCAI, 398–404. https://doi.org/10.24963/ijcai.2021/56

@inproceedings{ijcai2021p56,
  title     = {Vitality Indices are Equivalent to Induced Game-Theoretic Centralities},
  author    = {Skibski, Oskar},
  booktitle = {Proceedings of the Thirtieth International Joint Conference on
               Artificial Intelligence, {IJCAI-21}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Prof. Zhi-Hua Zhou},
  pages     = {398--404},
  year      = {2021},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2021/56},
  url       = {https://doi.org/10.24963/ijcai.2021/56},
}

TY  - CPAPER
TI  - Vitality Indices are Equivalent to Induced Game-Theoretic Centralities
AU  - Skibski, Oskar
T2  - Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI-21
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2021
SP  - 398
EP  - 404
DO  - 10.24963/ijcai.2021/56
UR  - https://doi.org/10.24963/ijcai.2021/56
ER  -