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Equilibria and Centrality in Link Formation Games

Author

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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

    as
    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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    4. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    5. 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.
    6. Zenou, Yves & Dequiedt, Vianney, 2014. "Local and Consistent Centrality Measures in Networks," Research Papers in Economics 2014:4, Stockholm University, Department of Economics.
    7. 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.
    8. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    9. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    11. Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 80(5), pages 1977-2016, September.
    12. Coralio Ballester & Marc Vorsatz, 2014. "Random Walk-Based Segregation Measures," The Review of Economics and Statistics, MIT Press, vol. 96(3), pages 383-401, July.
    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. 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.
    2. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    3. Koenig, Michael & Hsieh, Chih-Sheng & Liu, Xiaodong & Zimmermann, Christian, 2018. "Superstar Economists: Coauthorship networks and research output," CEPR Discussion Papers 13239, C.E.P.R. Discussion Papers.
    4. 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.
    5. Li, Xueheng, 2023. "Designing weighted and directed networks under complementarities," Games and Economic Behavior, Elsevier, vol. 140(C), pages 556-574.
    6. Hannu Salonen, 2015. "Bonacich Measures as Equilibria in Network Models," Discussion Papers 100, Aboa Centre for Economics.

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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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