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Equilibria and centrality in link formation games

Listed author(s):
  • 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.

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File URL: http://link.springer.com/10.1007/s00182-015-0514-6
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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 45 (2016)
Issue (Month): 4 (November)
Pages: 1133-1151

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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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  1. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
  2. 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.
  3. 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.
  4. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
  5. Dequiedt, Vianney & Zenou, Yves, 2014. "Local and Consistent Centrality Measures in Networks," CEPR Discussion Papers 10031, C.E.P.R. Discussion Papers.
  6. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 441-485.
  7. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
  8. 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.
  9. 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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