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Network games with incomplete information

Author

Listed:
  • Joan de Martí
  • Yves Zenou

    (GAINS - ARGUMANS - Atelier De Recherche En Gestion De L'université Du Mans - GAINS - Groupe d'Analyse des Itinéraires et des Niveaux Salariaux - UM - Le Mans Université)

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

  • Joan de Martí & Yves Zenou, 2015. "Network games with incomplete information," Post-Print hal-04329656, HAL.
    • Handle: RePEc:hal:journl:hal-04329656
    DOI: 10.1016/j.jmateco.2015.10.002
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    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. Zenou, Yves & Lindquist, Matthew, 2014. "Key Players in Co-Offending Networks," CEPR Discussion Papers 9889, C.E.P.R. Discussion Papers.
    3. 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.
    4. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Venkatesh Bala & Sanjeev Goyal, 1998. "Learning from Neighbours," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 595-621.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. 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.
    17. 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.
    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. 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.
    20. 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.
    21. 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.
    22. 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.
    23. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    24. Belhaj, Mohamed & Deroïan, Frédéric, 2013. "Strategic interaction and aggregate incentives," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 183-188.
    25. 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.
    26. 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.
    27. Galeotti, Andrea & Ghiglino, Christian & Squintani, Francesco, 2013. "Strategic information transmission networks," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1751-1769.
    28. Calvó-Armengol, Antoni & , & ,, 2015. "Communication and influence," Theoretical Economics, Econometric Society, vol. 10(2), May.
    29. 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.
    30. 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.
    31. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
    32. Zhou, Junjie & Chen, Ying-Ju, 2015. "Key leaders in social networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 212-235.
    33. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    34. 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.
    35. 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.
    36. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    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. 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.
    3. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    4. Andrea Galeotti & Benjamin Golub & Sanjeev Goyal, 2020. "Targeting Interventions in Networks," Econometrica, Econometric Society, vol. 88(6), pages 2445-2471, November.
    5. Julia Müller & Thorsten Upmann, 2017. "Eigenvalue Productivity: Measurement of Individual Contributions in Teams," CESifo Working Paper Series 6679, CESifo.
    6. Benjamin Golub & Stephen Morris, 2020. "Expectations, Networks, and Conventions," Papers 2009.13802, arXiv.org.
    7. 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.
    8. 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).
    9. Jan Gromadzki & Przemysław Siemaszko, 2022. "#IamLGBT: Social Networks and Coming Out," IBS Working Papers 06/2022, Instytut Badan Strukturalnych.
    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. Pellet, Thomas & Tahbaz-Salehi, Alireza, 2023. "Rigid production networks," Journal of Monetary Economics, Elsevier, vol. 137(C), pages 86-102.
    12. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    13. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    14. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    15. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.
    16. Leister, C. Matthew, 2020. "Information acquisition and welfare in network games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 453-475.
    17. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    18. Emerson Melo, 2018. "A Variational Approach to Network Games," Working Papers 2018.05, Fondazione Eni Enrico Mattei.
    19. 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.
    20. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    21. Promit K. Chaudhuri & Sudipta Sarangi & Hector Tzavellas, 2023. "Games Under Network Uncertainty," Papers 2305.03124, arXiv.org, revised Jul 2023.
    22. 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.

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    More about this item

    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

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