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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
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    References listed on IDEAS

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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.
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    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. Ben Golub & Yair Livne, 2010. "Strategic Random Networks," Working Papers 10-21, NET Institute.
    7. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    8. 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.
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    Citations

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    Cited by:

    1. Kenan Huremović, 2021. "A noncooperative model of contest network formation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 275-317, April.
    2. Isabel Melguizo, 2023. "Group representation concerns and network formation," Bulletin of Economic Research, Wiley Blackwell, vol. 75(1), pages 151-179, January.
    3. Leonardo Boncinelli & Alessio Muscillo & Paolo Pin, 2022. "Efficiency and Stability in a Process of Teams Formation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1101-1129, December.
    4. Péter Bayer & Ani Guerdjikova, 2020. "Optimism leads to optimality: Ambiguity in network formation," Working Papers hal-03005107, HAL.
    5. Jiménez-Martínez, Antonio & Melguizo-López, Isabel, 2022. "Making friends: The role of assortative interests and capacity constraints," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 431-465.
    6. Ryan Kor & Junjie Zhou, 2022. "Welfare and Distributional Effects of Joint Intervention in Networks," Papers 2206.03863, arXiv.org.
    7. Kinateder, Markus & Merlino, Luca Paolo, 2022. "Local public goods with weighted link formation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 316-327.
    8. Yang Sun & Wei Zhao & Junjie Zhou, 2023. "Structural Interventions In Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1533-1563, November.
    9. Norma Olaizola & Federico Valenciano, 2023. "A connections model with decreasing returns link-formation technology," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(1), pages 31-61, March.
    10. Norma Olaizola & Federico Valenciano, 2020. "Characterization of efficient networks in a generalized connections model with endogenous link strength," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 11(3), pages 341-367, September.
    11. Alan Griffith, 2022. "A continuous model of strong and weak ties," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1519-1563, December.
    12. Abbas Edalat & Samira Hossein Ghorban & Ali Ghoroghi, 2018. "Ex Post Nash Equilibrium in Linear Bayesian Games for Decision Making in Multi-Environments," Games, MDPI, vol. 9(4), pages 1-24, October.
    13. Li, Xueheng, 2023. "Designing weighted and directed networks under complementarities," Games and Economic Behavior, Elsevier, vol. 140(C), pages 556-574.
    14. Ding, Sihua, 2022. "Link investment substitutability: A factor influencing network formation," Games and Economic Behavior, Elsevier, vol. 136(C), pages 340-359.
    15. Tenev, Anastas P., 2020. "“Friends Are Thieves of Time": Heuristic Attention Sharing in Stable Friendship Networks," Research Memorandum 026, Maastricht University, Graduate School of Business and Economics (GSBE).
    16. Olaizola, Norma & Valenciano, Federico, 2020. "A connections model with decreasing returns link-formation technology," MPRA Paper 107585, University Library of Munich, Germany.

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    More about this item

    Keywords

    weighted networks; network formation; link-specific investment;
    All these keywords.

    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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