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A Model of Weighted Network Formation

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  • Baumann, L.

Abstract

The paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either “reciprocal” or “non-reciprocal”. In a reciprocal equilibrium, any two agents invest equally in the link between them. In a non-reciprocal equilibrium, agents are partitioned into “concentrated” and “diversified” agents and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and not efficient due to the positive externalities of investing in a link.

Suggested Citation

  • Baumann, L., 2019. "A Model of Weighted Network Formation," Cambridge Working Papers in Economics 1961, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1961
    Note: lb714
    as

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    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1961.pdf
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    References listed on IDEAS

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    1. Andrea Galeotti & Luca Paolo Merlino, 2014. "Endogenous Job Contact Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1201-1226, November.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. 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.
    4. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    5. Wang, Cheng & Lizardo, Omar & Hachen, David & Strathman, Anthony & Toroczkai, Zoltã N & Chawla, Nitesh V., 2013. "A dyadic reciprocity index for repeated interaction networks," Network Science, Cambridge University Press, vol. 1(1), pages 31-48, April.
    6. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
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    More about this item

    Keywords

    weighted networks; network formation; link-specific investment;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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