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Equilibria and centrality in link formation games

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  • Hannu Salonen

    (University of Turku)

Abstract

We study non-cooperative link formation games in which players have to decide how much to invest in connections 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. The utility from links is a weighted sum of Cobb–Douglas functions, the weights representing the common valuation. If the Cobb–Douglas functions are bilinear and the link formation cost is not too high, then indegree, eigenvector centrality, and the Katz–Bonacich centrality measure put the players in opposite order than the common valuation. The same result holds for non-negligible link formation costs if the Cobb–Douglas functions are separately concave but not jointly concave. If the Cobb–Douglas functions are strictly concave, then at the interior equilibrium these measures order the players in the same way as the common valuation.

Suggested Citation

  • Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0514-6
    DOI: 10.1007/s00182-015-0514-6
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    Cited by:

    1. 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.
    2. 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.
    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, 2018. "Superstar Economists: Coauthorship networks and research output," CEPR Discussion Papers 13239, C.E.P.R. Discussion Papers.
    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 networks;
    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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