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Equilibria and Centrality in Link Formation Games

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  • Hannu Salonen

    (Department of Economics, University of Turku)

Abstract

We study non-cooperative link formation games in which players have to decide how much to invest in relationships with other players. The relationship between equilibrium strategies and network centrality measures are investigated in games where there is a common valuation of players as friends. If the utility from relationships with other players is bilinear, then indegree, eigenvector centrality, and the Katz-Bonacich centrality measure put the players in opposite order than the common valuation. If the utility from relationships is strictly concave, then these measures order the players in the same way as the common valuation.

Suggested Citation

  • Hannu Salonen, 2014. "Equilibria and Centrality in Link Formation Games," Discussion Papers 92, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp92
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    References listed on IDEAS

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    1. 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.
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    7. Zenou, Yves & ,, 2014. "Local and Consistent Centrality Measures in Networks," CEPR Discussion Papers 10031, C.E.P.R. Discussion Papers.
    8. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Du, Ye & Lehrer, Ehud & Pauzner, Ady, 2015. "Competitive economy as a ranking device over networks," Games and Economic Behavior, Elsevier, vol. 91(C), pages 1-13.
    10. Hannu Salonen, 2015. "Reciprocal Equilibria in Link Formation Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(3), pages 169-183, December.
    11. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    12. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    13. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
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    Cited by:

    1. Hsieh, Chih-Sheng & König, Michael D. & Liu, Xiaodong & Zimmermann, Christian, 2018. "Superstar Economists: Coauthorship Networks and Research Output," IZA Discussion Papers 11916, Institute of Labor Economics (IZA).
    2. Hannu Salonen, 2015. "Reciprocal Equilibria in Link Formation Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(3), pages 169-183, December.
    3. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    4. Koenig, Michael & Hsieh, Chih-Sheng & Liu, Xiaodong & Zimmermann, Christian, 2020. "Collaboration in Bipartite Networks, with an Application to Coauthorship Networks," CEPR Discussion Papers 15195, C.E.P.R. Discussion Papers.
    5. Hannu Salonen, 2015. "Bonacich Measures as Equilibria in Network Models," Discussion Papers 100, Aboa Centre for Economics.
    6. Li, Xueheng, 2023. "Designing weighted and directed networks under complementarities," Games and Economic Behavior, Elsevier, vol. 140(C), pages 556-574.

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    More about this item

    Keywords

    link formation games; centrality measures; complete network;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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