IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v61y2015icp221-240.html
   My bibliography  Save this article

Network games with incomplete information

Author

Listed:
  • de Martí, Joan
  • Zenou, Yves

Abstract

We consider a network game with strategic complementarities where the individual reward or the strength of interactions is only partially known by the agents. Players receive different correlated signals and they make inferences about other players’ information. We demonstrate that there exists a unique Bayesian-Nash equilibrium. We characterize the equilibrium by disentangling the information effects from the network effects and show that the equilibrium effort of each agent is a weighted combinations of different Katz–Bonacich centralities.

Suggested Citation

  • de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    • Handle: RePEc:eee:mateco:v:61:y:2015:i:c:p:221-240
    DOI: 10.1016/j.jmateco.2015.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815001202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2015.10.002?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jeanne Hagenbach & Frédéric Koessler, 2010. "Strategic Communication Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1072-1099.
    2. Lawrence E. Blume & William A. Brock & Steven N. Durlauf & Rajshri Jayaraman, 2015. "Linear Social Interactions Models," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 444-496.
    3. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    4. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    7. Venkatesh Bala & Sanjeev Goyal, 1998. "Learning from Neighbours," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 595-621.
    8. Matthew Elliott & Benjamin Golub & Matthew O. Jackson, 2014. "Financial Networks and Contagion," American Economic Review, American Economic Association, vol. 104(10), pages 3115-3153, October.
    9. 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.
    10. 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.
    11. Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2011. "Bayesian Learning in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1201-1236.
    12. van Heumen, R.W.J. & Peleg, B. & Tijs, S.H. & Borm, P.E.M., 1994. "Axiomatic characterizations of solutions for Bayesian games," Other publications TiSEM b16fc7d9-aee7-4f36-95f2-3, Tilburg University, School of Economics and Management.
    13. Benjamin Golub & Matthew O. Jackson, 2012. "How Homophily Affects the Speed of Learning and Best-Response Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1287-1338.
    14. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    15. 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.
    16. 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.
    17. Denbee, Edward & Julliard, Christian & Li, Ye & Yuan, Kathy, 2021. "Network risk and key players: A structural analysis of interbank liquidity," Journal of Financial Economics, Elsevier, vol. 141(3), pages 831-859.
    18. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 218-244.
    19. Antoni Calvó-Armengol & Yves Zenou, 2004. "Social Networks And Crime Decisions: The Role Of Social Structure In Facilitating Delinquent Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(3), pages 939-958, August.
    20. Belhaj, Mohamed & Deroïan, Frédéric, 2013. "Strategic interaction and aggregate incentives," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 183-188.
    21. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    22. Takashi Ui, 2009. "Bayesian potentials and information structures: Team decision problems revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 271-291, September.
    23. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
    24. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2014. "Endogenous peer effects: local aggregate or local average?," Journal of Economic Behavior & Organization, Elsevier, vol. 103(C), pages 39-59.
    25. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
    26. Zhou, Junjie & Chen, Ying-Ju, 2015. "Key leaders in social networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 212-235.
    27. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    28. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    29. Zenou, Yves & Lindquist, Matthew, 2014. "Key Players in Co-Offending Networks," CEPR Discussion Papers 9889, C.E.P.R. Discussion Papers.
    30. 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.
    31. Zenou, Yves & Patacchini, Eleonora & Cohen-Cole, Ethan, 2011. "Systemic Risk and Network Formation in the Interbank Market," CEPR Discussion Papers 8332, C.E.P.R. Discussion Papers.
    32. Galeotti, Andrea & Ghiglino, Christian & Squintani, Francesco, 2013. "Strategic information transmission networks," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1751-1769.
    33. Calvó-Armengol, Antoni & , & ,, 2015. "Communication and influence," Theoretical Economics, Econometric Society, vol. 10(2), May.
    34. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    35. de Martí Beltran, Joan, 2009. "Matthew O. Jackson, Social and Economic Networks , Princeton University Press (2008)," Regional Science and Urban Economics, Elsevier, vol. 39(5), pages 644-645, September.
    36. Manning Li & Jihong Liu, 2014. "Discussion and Implications," SpringerBriefs in Business, in: Innovative Advisory Services in the Virtual World, edition 127, chapter 0, pages 51-63, Springer.
    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. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    2. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    3. Benjamin Golub & Stephen Morris, 2020. "Expectations, Networks, and Conventions," Papers 2009.13802, arXiv.org.
    4. Mariann Ollar & Antonio Penta, 2021. "A network solution to robust implementation: The case of identical but unknown distributions," Economics Working Papers 1776, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Zhu, Haoruo & Ni, Yaodong & Yang, Meng & Song, Qinyu, 2023. "Blessing or curse? Impact of incomplete information in a networked cournot competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    6. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    7. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    8. Andrea Galeotti & Benjamin Golub & Sanjeev Goyal, 2020. "Targeting Interventions in Networks," Econometrica, Econometric Society, vol. 88(6), pages 2445-2471, November.
    9. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    10. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.
    11. Leister, C. Matthew, 2020. "Information acquisition and welfare in network games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 453-475.
    12. 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.
    13. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    14. Ryo Itoh & Zonghui Li, 2021. "Effects of dual networks on tax strategies: geography and transaction," The Japanese Economic Review, Springer, vol. 72(1), pages 97-128, January.
    15. Chen, Hong & Lam, Jasmine Siu Lee & Liu, Nan, 2018. "Strategic investment in enhancing port–hinterland container transportation network resilience: A network game theory approach," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 83-112.
    16. Julia Müller & Thorsten Upmann, 2017. "Eigenvalue Productivity: Measurement of Individual Contributions in Teams," CESifo Working Paper Series 6679, CESifo.
    17. Jan Gromadzki & Przemysław Siemaszko, 2022. "#IamLGBT: Social Networks and Coming Out," IBS Working Papers 06/2022, Instytut Badan Strukturalnych.
    18. Pellet, Thomas & Tahbaz-Salehi, Alireza, 2023. "Rigid production networks," Journal of Monetary Economics, Elsevier, vol. 137(C), pages 86-102.
    19. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    20. Emerson Melo, 2018. "A Variational Approach to Network Games," Working Papers 2018.05, Fondazione Eni Enrico Mattei.
    21. Belhaj, Mohamed & Deroïan, Frédéric, 2021. "The value of network information: Assortative mixing makes the difference," Games and Economic Behavior, Elsevier, vol. 126(C), pages 428-442.
    22. Promit K. Chaudhuri & Sudipta Sarangi & Hector Tzavellas, 2023. "Games Under Network Uncertainty," Papers 2305.03124, arXiv.org, revised Jul 2023.

    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. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    3. Hahn, Youjin & Islam, Asadul & Patacchini, Eleonora & Zenou, Yves, 2015. "Network Structure and Education Outcomes: Evidence from a Field Experiment in Bangladesh," IZA Discussion Papers 8872, Institute of Labor Economics (IZA).
    4. 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.
    5. Zenou, Yves & Patacchini, Eleonora & Islam, Asad, 2015. "Teams, Organization and Education Outcomes: Evidence from a field experiment in Bangladesh," CEPR Discussion Papers 10631, C.E.P.R. Discussion Papers.
    6. Zenou, Yves & Chen, Ying-Ju & Zhou, Junjie, 2015. "Multiple Activities for Socially-Connected Criminals," CEPR Discussion Papers 10709, C.E.P.R. Discussion Papers.
    7. Zenou, Yves & Lindquist, Matthew & Sauermann, Jan, 2015. "Network Effects on Worker Productivity," CEPR Discussion Papers 10928, C.E.P.R. Discussion Papers.
    8. Zenou, Yves, 2012. "Networks in Economics," CEPR Discussion Papers 9021, C.E.P.R. Discussion Papers.
    9. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2016. "Networks: An Economic Perspective," Papers 1608.07901, arXiv.org.
    10. 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.
    11. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    12. Zenou, Yves & Olcina, Gonzalo & Panebianco, Fabrizio, 2017. "Conformism, Social Norms and the Dynamics of Assimilation," CEPR Discussion Papers 12166, C.E.P.R. Discussion Papers.
    13. 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.
    14. Díaz, Carlos & Patacchini, Eleonora & Verdier, Thierry & Zenou, Yves, 2021. "Leaders in juvenile crime," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 638-667.
    15. repec:spo:wpmain:info:hdl:2441/78vacv4udu92eq3fec89svm9uv is not listed on IDEAS
    16. repec:hal:spmain:info:hdl:2441/78vacv4udu92eq3fec89svm9uv is not listed on IDEAS
    17. Cohen-Cole, Ethan & Patacchini, Eleonora & Zenou, Yves, 2015. "Static and dynamic networks in interbank markets," Network Science, Cambridge University Press, vol. 3(1), pages 98-123, March.
    18. Patacchini, Eleonora & Rainone, Edoardo & Zenou, Yves, 2017. "Heterogeneous peer effects in education," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 190-227.
    19. Helsley, Robert W. & Zenou, Yves, 2014. "Social networks and interactions in cities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 426-466.
    20. Yann Algan & Quoc-Anh Do & Nicolò Dalvit & Alexis Le Chapelain & Yves Zenou, 2015. "How Social Networks Shape Our Beliefs: A Natural Experiment among Future French Politicians," Working Papers hal-03459820, HAL.
    21. de Marti, Joan & Zenou, Yves, 2009. "Social Networks," Working Paper Series 816, Research Institute of Industrial Economics.
    22. Lindquist, Matthew J. & Zenou, Yves, 2019. "Crime and Networks: 10 Policy Lessons," IZA Discussion Papers 12534, Institute of Labor Economics (IZA).

    More about this item

    Keywords

    Social networks; Strategic complementarities; Bayesian games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    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:eee:mateco:v:61:y:2015:i:c:p:221-240. 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.