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The Evolution of Networks and Local Public Good Provision: A Potential Approach

Author

Listed:
  • Markus Kinateder

    (Departamento de Economía, Edificio Amigos, Universidad de Navarra, 31009 Pamplona, Spain
    These authors contributed equally to this work.)

  • Luca Paolo Merlino

    (Department of Economics, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp.

Suggested Citation

  • Markus Kinateder & Luca Paolo Merlino, 2021. "The Evolution of Networks and Local Public Good Provision: A Potential Approach," Games, MDPI, vol. 12(3), pages 1-12, July.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:3:p:55-:d:587308
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    References listed on IDEAS

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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. Kinateder, Markus & Merlino, Luca Paolo, 2023. "Free riding in networks," European Economic Review, Elsevier, vol. 152(C).
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    5. 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(4), pages 1201-1226, November.
    6. 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.
    7. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
    8. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    9. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    10. 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.
    11. Cui, Zhiwei & Weidenholzer, Simon, 2021. "Lock-in through passive connections," Journal of Economic Theory, Elsevier, vol. 192(C).
    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. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    14. Staudigl, Mathias & Weidenholzer, Simon, 2014. "Constrained interactions and social coordination," Journal of Economic Theory, Elsevier, vol. 152(C), pages 41-63.
    15. Ryo Nakajima, 2007. "Measuring Peer Effects on Youth Smoking Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 897-935.
    16. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    17. Merlino, Luca Paolo, 2019. "Informal job search through social networks and vacancy creation," Economics Letters, Elsevier, vol. 178(C), pages 82-85.
    18. Staudigl, Mathias, 2011. "Potential games in volatile environments," Games and Economic Behavior, Elsevier, vol. 72(1), pages 271-287, May.
    19. Chih-Sheng Hsieh & Michael D. Konig & Xiaodong Liu, 2022. "A Structural Model for the Coevolution of Networks and Behavior," The Review of Economics and Statistics, MIT Press, vol. 104(2), pages 355-367, May.
    20. Angelo Mele, 2017. "A Structural Model of Dense Network Formation," Econometrica, Econometric Society, vol. 85, pages 825-850, May.
    21. repec:esx:essedp:747 is not listed on IDEAS
    22. ,, 2015. "Social activity and network formation," Theoretical Economics, Econometric Society, vol. 10(2), May.
    23. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    24. 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.
    25. Hiller, Timo, 2017. "Peer effects in endogenous networks," Games and Economic Behavior, Elsevier, vol. 105(C), pages 349-367.
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    Cited by:

    1. Philip Solimine & Luke Boosey, 2021. "Strategic formation of collaborative networks," Papers 2109.14204, arXiv.org, revised Apr 2024.
    2. Kinateder, Markus & Merlino, Luca Paolo, 2023. "Free riding in networks," European Economic Review, Elsevier, vol. 152(C).
    3. Gianpiero Monaco & Luca Moscardelli & Yllka Velaj, 2021. "Additively Separable Hedonic Games with Social Context," Games, MDPI, vol. 12(3), pages 1-14, September.

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