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The Bonacich Shapley centrality

Author

Listed:
  • Nizar Allouch
  • A. Meca
  • K. Polotskaya

Abstract

In this paper, we develop a new game theoretic network centrality measure based on the Shapley value. To do so, we consider a coalitional game, where the worth of each coalition is the total play in the game introduced in Ballester et al. (2006). We first establish that the game is convex. As a consequence, the Shapley value belongs to the core, which enhances the attractive features of our new centrality measure. Then, we compute the Shapley value for various examples and illustrate some of its properties.

Suggested Citation

  • Nizar Allouch & A. Meca & K. Polotskaya, 2021. "The Bonacich Shapley centrality," Studies in Economics 2106, School of Economics, University of Kent.
    • Handle: RePEc:ukc:ukcedp:2106
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    File URL: https://www.kent.ac.uk/economics/repec/2106.pdf
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    References listed on IDEAS

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    1. Lindelauf, R.H.A. & Hamers, H.J.M. & Husslage, B.G.M., 2013. "Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda," European Journal of Operational Research, Elsevier, vol. 229(1), pages 230-238.
    2. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    3. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    4. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
    5. Hellmann, Tim, 2021. "Pairwise stable networks in homogeneous societies with weak link externalities," European Journal of Operational Research, Elsevier, vol. 291(3), pages 1164-1179.
    6. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
    7. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
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    More about this item

    Keywords

    Social networks; network games; peer effects; centrality measures; Bonacich centrality; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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