IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v2y2011i3p302-332d13673.html

The Price of Anarchy for Network Formation in an Adversary Model

Author

Listed:
  • Lasse Kliemann

    (Department of Computer Science, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, Kiel 24098, Germany)

Abstract

We study network formation with n players and link cost α > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player ν incorporates the expected number of players to which ν will become disconnected. We focus on unilateral link formation and Nash equilibrium . We show existence of Nash equilibria and a price of stability of 1 + ο (1) under moderate assumptions on the adversary and n ≥ 9. We prove bounds on the price of anarchy for two special adversaries: one removes a link chosen uniformly at random, while the other removes a link that causes a maximum number of player pairs to be separated. We show an Ο (1) bound on the price of anarchy for both adversaries, the constant being bounded by 15 + ο (1) and 9 + ο (1), respectively.

Suggested Citation

  • Lasse Kliemann, 2011. "The Price of Anarchy for Network Formation in an Adversary Model," Games, MDPI, vol. 2(3), pages 1-31, August.
    • Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:302-332:d:13673
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/2/3/302/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/2/3/302/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Johari, Ramesh & Mannor, Shie & Tsitsiklis, John N., 2006. "A contract-based model for directed network formation," Games and Economic Behavior, Elsevier, vol. 56(2), pages 201-224, August.
    2. Sudipta Sarangi & H. Haller, 2003. "Nash Networks with Heterogeneous Agents," Departmental Working Papers 2003-06, Department of Economics, Louisiana State University.
    3. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
    6. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
    7. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
    8. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    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. Lasse Kliemann & Elmira Shirazi Sheykhdarabadi & Anand Srivastav, 2017. "Swap Equilibria under Link and Vertex Destruction," Games, MDPI, vol. 8(1), pages 1-18, February.

    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. Jun, Tackseung & Kim, Jeong-Yoo, 2007. "Connectivity, stability and efficiency in a network as an information flow," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 314-331, May.
    2. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    3. Block, Lukas, 2023. "Network formation with NIMBY constraints," Energy Economics, Elsevier, vol. 119(C).
    4. Lukas Block, 2022. "Network formation with NIMBY constraints," Working Papers Dissertations 94, Paderborn University, Faculty of Business Administration and Economics.
    5. Gilles, R.P. & Sarangi, S., 2003. "The Role of Trust in Costly Network Formation," Discussion Paper 2003-53, Tilburg University, Center for Economic Research.
    6. Michael Caldara & Michael McBride, 2014. "An Experimental Study of Network Formation with Limited Observation," Working Papers 141501, University of California-Irvine, Department of Economics.
    7. Safi, Shahir, 2022. "Listen before you link: Optimal monitoring rules for communication networks," Games and Economic Behavior, Elsevier, vol. 133(C), pages 230-247.
    8. Gao Hongwei & Qiao Han & Sedakov Artem & Wang Lei, 2015. "A Dynamic Formation Procedure of Information Flow Networks," Journal of Systems Science and Information, De Gruyter, vol. 3(2), pages 97-110, April.
    9. Breitmoser, Yves & Vorjohann, Pauline, 2013. "Efficient structure of noisy communication networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 396-409.
    10. Philippe Bich & Lisa Morhaim, 2020. "On the Existence of Pairwise Stable Weighted Networks," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1393-1404, November.
    11. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    12. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    13. Dev, Pritha, 2010. "Choosing `Me' and `My Friends': Identity in a Non-Cooperative Network Formation Game with Cost Sharing," MPRA Paper 21631, University Library of Munich, Germany.
    14. Yangbo Song & Mihaela Schaar, 2015. "Dynamic network formation with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 301-331, June.
    15. Ping Sun & Elena Parilina, 2024. "Dynamic Network Formation with Ordered Partitioning and Incomplete Information," Dynamic Games and Applications, Springer, vol. 14(4), pages 921-958, September.
    16. Pongou, Roland & Serrano, Roberto, 2016. "Volume of trade and dynamic network formation in two-sided economies," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 147-163.
    17. Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 211-237, February.
    18. Andreas Bjerre-Nielsen, 2015. "Sorting in Networks: Adversity and Structure," Papers 1503.07389, arXiv.org, revised Aug 2017.
    19. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    20. Berno Buechel & Tim Hellmann, 2012. "Under-connected and over-connected networks: the role of externalities in strategic network formation," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 71-87, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jgames:v:2:y:2011:i:3:p:302-332:d:13673. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.