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A connections model with decreasing returns link-formation technology

Author

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  • Norma Olaizola

    (Universidad del País Vasco UPV/EHU)

  • Federico Valenciano

    (Universidad del País Vasco UPV/EHU)

Abstract

We study a connections model where the strength of a link depends on the amount invested in it and is determined by an increasing strictly concave function. The revenue from investments in links is the value (information, contacts, friendship) that the nodes receive through the network. First, assuming that links are the result of investments by the node-players involved, there is the question of stability. We introduce and characterize a notion of marginal equilibrium, where all nodes play locally best responses, and identify different marginally stable structures. This notion is based on weak assumptions about node-players’ information and is necessary for Nash equilibrium and for pairwise stability. Second, efficient networks in absolute terms are characterized. Efficiency and stability are shown to be incompatible, but partial subsidizing is shown to be able to bridge the gap.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:series:v:14:y:2023:i:1:d:10.1007_s13209-022-00266-8
    DOI: 10.1007/s13209-022-00266-8
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    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.
    2. Vincent Boucher, 2015. "Structural Homophily," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(1), pages 235-264, February.
    3. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, May.
    4. Sanjeev Goyal, 2007. "Introduction to Connections: An Introduction to the Economics of Networks," Introductory Chapters, in: Connections: An Introduction to the Economics of Networks, Princeton University Press.
    5. repec:ehu:ikerla:19437 is not listed on IDEAS
    6. Feri, Francesco, 2007. "Stochastic stability in networks with decay," Journal of Economic Theory, Elsevier, vol. 135(1), pages 442-457, July.
    7. Francesco Feri & Miguel Meléndez-Jiménez, 2013. "Coordination in evolving networks with endogenous decay," Journal of Evolutionary Economics, Springer, vol. 23(5), pages 955-1000, November.
    8. 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.
    9. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    10. Vincent Boucher, 2015. "Structural Homophily," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 235-264, February.
    11. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    12. Harmsen - van Hout, Marjolein J.W. & Herings, P. Jean-Jacques & Dellaert, Benedict G.C., 2013. "Communication network formation with link specificity and value transferability," European Journal of Operational Research, Elsevier, vol. 229(1), pages 199-211.
    13. Deroian, F., 2009. "Endogenous link strength in directed communication networks," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 110-116, January.
    14. 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.
    15. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    16. Olaizola, By Norma & Valenciano, Federico, 2021. "Efficiency and stability in the connections model with heterogeneous nodes," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 490-503.
    17. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, May.
    18. Baumann, Leonie, 2021. "A model of weighted network formation," Theoretical Economics, Econometric Society, vol. 16(1), January.
    19. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    20. 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.
    21. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
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    Cited by:

    1. Olaizola, Norma & Valenciano, Federico, 2024. "Core–periphery and nested networks emerging from a simple model of network formation," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 42-51.

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    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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