IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v99y2022ics0304406821001646.html
   My bibliography  Save this article

A simple model of network formation with competition effects

Author

Listed:
  • Hiller, Timo

Abstract

This paper provides a game-theoretic model of network formation with a continuous effort choice. Efforts are strategic complements for direct neighbors in the network and display global substitution/competition effects. We show that if the parameter governing local strategic complements is larger than the one governing global strategic substitutes, then all pairwise Nash equilibrium networks are nested split graphs. We also consider the problem of a planner, who can choose effort levels and place links according to a network cost function. Again all socially optimal configurations are such that the network is a nested split graph. However, the socially optimal network may be different from equilibrium networks and efficient effort levels do not coincide with Nash equilibrium effort levels. In the presence of strategic substitutes, Nash equilibrium effort levels may be too high or too low relative to efficient effort levels. The relevant applications are crime networks and R&D collaborations among firms, but also interbank lending and trade.

Suggested Citation

  • Hiller, Timo, 2022. "A simple model of network formation with competition effects," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:mateco:v:99:y:2022:i:c:s0304406821001646
    DOI: 10.1016/j.jmateco.2021.102611
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821001646
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102611?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mario V. Tomasello & Mauro Napoletano & Antonios Garas & Frank Schweitzer, 2017. "The rise and fall of R&D networks," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(4), pages 617-646.
    2. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    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. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2010. "Delinquent Networks," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 34-61, March.
    5. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    6. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    7. Markus Kinateder & Luca Paolo Merlino, 2017. "Public Goods in Endogenous Networks," American Economic Journal: Microeconomics, American Economic Association, vol. 9(3), pages 187-212, August.
    8. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    9. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2017. "The Economic Consequences of Social-Network Structure," Journal of Economic Literature, American Economic Association, vol. 55(1), pages 49-95, March.
    10. Chih-Sheng Hsieh & Michael D. König & Xiaodong Liu, 2012. "Network formation with local complements and global substitutes: the case of R&D networks," ECON - Working Papers 217, Department of Economics - University of Zurich, revised Feb 2017.
    11. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    12. Andrea Galeotti & Sanjeev Goyal, 2010. "The Law of the Few," American Economic Review, American Economic Association, vol. 100(4), pages 1468-1492, September.
    13. Eleonora Patacchini & Yves Zenou, 2012. "Juvenile Delinquency and Conformism," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 28(1), pages 1-31.
    14. Billand, Pascal & Bravard, Christophe & Durieu, Jacques & Sarangi, Sudipta, 2015. "Efficient networks for a class of games with global spillovers," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 203-210.
    15. Helsley, Robert W. & Zenou, Yves, 2014. "Social networks and interactions in cities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 426-466.
    16. Belhaj, Mohamed & Bervoets, Sebastian & Deroïan, Frédéric, 2016. "Efficient networks in games with local complementarities," Theoretical Economics, Econometric Society, vol. 11(1), January.
    17. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    18. Christophe Bravard & Sudipta Sarangi & SUMIT JOSHI & AHMED SABER MAHMUD, 2016. "Network Formation under Multiple Sources of Externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(2), pages 148-167, April.
    19. Bastian Westbrock, 2010. "Natural concentration in industrial research collaboration," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 351-371, June.
    20. Hiller, Timo, 2017. "Peer effects in endogenous networks," Games and Economic Behavior, Elsevier, vol. 105(C), pages 349-367.
    21. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Topa, Giorgio & Zenou, Yves, 2015. "Neighborhood and Network Effects," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 561-624, Elsevier.
    3. Yang Sun & Wei Zhao & Junjie Zhou, 2021. "Structural Interventions in Networks," Papers 2101.12420, arXiv.org, revised Feb 2021.
    4. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    5. Zenou, Yves & Lindquist, Matthew & Sauermann, Jan, 2015. "Network Effects on Worker Productivity," CEPR Discussion Papers 10928, C.E.P.R. Discussion Papers.
    6. Kinateder, Markus & Merlino, Luca Paolo, 2023. "Free riding in networks," European Economic Review, Elsevier, vol. 152(C).
    7. Hiller, Timo, 2017. "Peer effects in endogenous networks," Games and Economic Behavior, Elsevier, vol. 105(C), pages 349-367.
    8. Norma Olaizola & Federico Valenciano, 2020. "Dominance of weighted nested split graph networks in connections models," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 75-96, March.
    9. Timo Hiller, 2017. "Too Big to Jail? Key-Player Policies When the Network is Endogenous," Bristol Economics Discussion Papers 17/693, School of Economics, University of Bristol, UK.
    10. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    11. Allouch, Nizar, 2017. "The cost of segregation in (social) networks," Games and Economic Behavior, Elsevier, vol. 106(C), pages 329-342.
    12. Chen, Ying-Ju & Zenou, Yves & Zhou, Junjie, 2022. "The impact of network topology and market structure on pricing," Journal of Economic Theory, Elsevier, vol. 204(C).
    13. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    14. Ushchev, Philip & Zenou, Yves, 2018. "Price competition in product variety networks," Games and Economic Behavior, Elsevier, vol. 110(C), pages 226-247.
    15. Olaizola Ortega, María Norma & Valenciano Llovera, Federico, 2017. "Efficiency of weighted networks," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    16. 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.
    17. Zenou, Yves & Chen, Ying-Ju & Zhou, Junjie, 2020. "Network Topology and Market Structure," CEPR Discussion Papers 14495, C.E.P.R. Discussion Papers.
    18. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves & Lee, Lung-Fei, 2011. "Criminal Networks: Who is the Key Player?," Research Papers in Economics 2011:7, Stockholm University, Department of Economics.
    19. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    20. Harkins, Andrew, 2020. "Network Comparative Statics," The Warwick Economics Research Paper Series (TWERPS) 1306, University of Warwick, Department of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:99:y:2022:i:c:s0304406821001646. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.