IDEAS home Printed from https://ideas.repec.org/p/fem/femwpa/2018.05.html
   My bibliography  Save this paper

A Variational Approach to Network Games

Author

Listed:
  • Emerson Melo

    (Indiana University, Department of Economics)

Abstract

This paper studies strategic interaction in networks. We focus on games of strategic substitutes and strategic complements, and departing from previous literature, we do not assume particular functional forms on players' payoffs. By exploiting variational methods, we show that the uniqueness, the comparative statics, and the approximation of a Nash equilibrium are determined by a precise relationship between the lowest eigenvalue of the network, a measure of players' payoff concavity, and a parameter capturing the strength of the strategic interaction among players. We apply our framework to the study of aggregative network games, games of mixed interactions, and Bayesian network games.

Suggested Citation

  • Emerson Melo, 2018. "A Variational Approach to Network Games," Working Papers 2018.05, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2018.05
    as

    Download full text from publisher

    File URL: https://feem-media.s3.eu-central-1.amazonaws.com/wp-content/uploads/NDL2018-005.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    2. 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.
    3. Michael D. König & Dominic Rohner & Mathias Thoenig & Fabrizio Zilibotti, 2017. "Networks in Conflict: Theory and Evidence From the Great War of Africa," Econometrica, Econometric Society, vol. 85, pages 1093-1132, July.
    4. Yann Bramoullé & Andrea Galeotti & Brian Rogers, 2016. "The Oxford Handbook of the Economics of Networks," Post-Print hal-01447842, HAL.
    5. Yann Bramoullé & Andrea Galeotti & Brian Rogers, 2016. "The Oxford Handbook of the Economics of Networks," Post-Print hal-03572533, HAL.
    6. 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.
    7. Ballester, Coralio & Calvó-Armengol, Antoni, 2010. "Interactions with hidden complementarities," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 397-406, November.
    8. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    9. 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.
    10. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    11. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Belhaj, Mohamed & Bramoullé, Yann & Deroïan, Frédéric, 2014. "Network games under strategic complementarities," Games and Economic Behavior, Elsevier, vol. 88(C), pages 310-319.
    13. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    14. 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.
    15. ,, 2015. "Social activity and network formation," Theoretical Economics, Econometric Society, vol. 10(2), May.
    16. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    17. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    18. Archer, Aaron & Kleinberg, Robert, 2014. "Truthful germs are contagious: A local-to-global characterization of truthfulness," Games and Economic Behavior, Elsevier, vol. 86(C), pages 340-366.
    19. Lavi, Ron & Swamy, Chaitanya, 2009. "Truthful mechanism design for multidimensional scheduling via cycle monotonicity," Games and Economic Behavior, Elsevier, vol. 67(1), pages 99-124, September.
    20. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    21. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, September.
    22. Hiller, Timo, 2017. "Peer effects in endogenous networks," Games and Economic Behavior, Elsevier, vol. 105(C), pages 349-367.
    23. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaowei Hu & Peng Li, 2021. "Relief and Stimulus in A Cross-sector Multi-product Scarce Resource Supply Chain Network," Papers 2101.09373, arXiv.org, revised Nov 2022.
    2. Allouch, Nizar & King, Maia, 2021. "Welfare targeting in networks," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. Parise, Francesca & Ozdaglar, Asuman, 2019. "A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis," Games and Economic Behavior, Elsevier, vol. 114(C), pages 47-82.
    4. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    5. Nizar Allouch & Maia King, 2019. "Constrained public goods in networks," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(5), pages 895-902, October.
    6. Hu, Xiaowei & Li, Peng, 2022. "Relief and stimulus in a cross-sector multi-product scarce resource supply chain network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    7. Luke A. Boosey & Christopher Brown, 2021. "Contests with Network Externalities: Theory & Evidence," Working Papers wp2021_07_02, Department of Economics, Florida State University.

    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. Parise, Francesca & Ozdaglar, Asuman, 2019. "A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis," Games and Economic Behavior, Elsevier, vol. 114(C), pages 47-82.
    2. Zenou, Yves & Bochet, Olivier & Faure, Mathieu & Long, Yan, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    3. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    4. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    5. Bochet, Olivier & Faure, Mathieu & Long, Yan & Zenou, Yves, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    6. 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.
    7. 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.
    8. Ashani Amarasinghe & Roland Hodler & Paul A. Raschky & Yves Zenou, 2018. "Spatial Diffusion of Economic Shocks in Networks," CESifo Working Paper Series 7001, CESifo.
    9. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald & Thuijsman, Frank, 2019. "Adaptive learning in weighted network games," Journal of Economic Dynamics and Control, Elsevier, vol. 105(C), pages 250-264.
    10. Zenou, Yves & Lindquist, Matthew & Sauermann, Jan, 2015. "Network Effects on Worker Productivity," CEPR Discussion Papers 10928, C.E.P.R. Discussion Papers.
    11. Andrea Galeotti & Benjamin Golub & Sanjeev Goyal, 2020. "Targeting Interventions in Networks," Econometrica, Econometric Society, vol. 88(6), pages 2445-2471, November.
    12. Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    13. Jadbabaie, Ali & Kakhbod, Ali, 2019. "Optimal contracting in networks," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1094-1153.
    14. Belhaj, Mohamed & Bramoullé, Yann & Deroïan, Frédéric, 2014. "Network games under strategic complementarities," Games and Economic Behavior, Elsevier, vol. 88(C), pages 310-319.
    15. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    16. Ushchev, Philip & Zenou, Yves, 2018. "Price competition in product variety networks," Games and Economic Behavior, Elsevier, vol. 110(C), pages 226-247.
    17. Yang Sun & Wei Zhao & Junjie Zhou, 2021. "Structural Interventions in Networks," Papers 2101.12420, arXiv.org, revised Feb 2021.
    18. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    19. Hiller, Timo, 2022. "A simple model of network formation with competition effects," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    20. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.

    More about this item

    Keywords

    Network Games; Variational Inequalities; Lowest Eigenvalue; Shock Propagation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:fem:femwpa:2018.05. 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: Alberto Prina Cerai (email available below). General contact details of provider: https://edirc.repec.org/data/feemmit.html .

    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.