IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v38y2019i1d10.1007_s10878-018-0366-7.html
   My bibliography  Save this article

Hitting a path: a generalization of weighted connectivity via game theory

Author

Listed:
  • Dávid Szeszlér

    (Budapest University of Technology and Economics)

Abstract

Applying game-theoretical tools for measuring the reliability of a network has become very common. The basic idea is very natural: analyzing an appropriately defined attacker–defender game might give rise to a relevant security metric. In this paper we consider a very natural set of games: the Defender chooses a path P between two given nodes and the Attacker chooses a network element a (that is, an edge or a node). In all cases, the Attacker has to pay a given cost of attack c(a); if, however, a is on P then he also gains a given profit of d(a). We determine the value of various versions of this game and show that the thus arising reliability metrics provide a generalization of weighted connectivity of graphs. We also prove that the values of the games and optimum mixed strategies for both players can be computed in strongly polynomial time.

Suggested Citation

  • Dávid Szeszlér, 2019. "Hitting a path: a generalization of weighted connectivity via game theory," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 72-85, July.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0366-7
    DOI: 10.1007/s10878-018-0366-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0366-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-018-0366-7?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
    Full references (including those not matched with items on IDEAS)

    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. Laan, Corine M. & van der Mijden, Tom & Barros, Ana Isabel & Boucherie, Richard J. & Monsuur, Herman, 2017. "An interdiction game on a queueing network with multiple intruders," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1069-1080.
    2. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    3. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.
    4. José Correa & Tobias Harks & Vincent J. C. Kreuzen & Jannik Matuschke, 2017. "Fare Evasion in Transit Networks," Operations Research, INFORMS, vol. 65(1), pages 165-183, February.
    5. Michael P. Atkinson & Lawrence M. Wein, 2008. "TECHNICAL NOTE---Spatial Queueing Analysis of an Interdiction System to Protect Cities from a Nuclear Terrorist Attack," Operations Research, INFORMS, vol. 56(1), pages 247-254, February.
    6. Qizhi Fang & Bo Li & Xiaohan Shan & Xiaoming Sun, 2018. "Path cooperative games," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 211-229, July.
    7. Zhang, Jing & Zhuang, Jun & Behlendorf, Brandon, 2018. "Stochastic shortest path network interdiction with a case study of Arizona–Mexico border," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 62-73.
    8. Bloch, Francis & Chatterjee, Kalyan & Dutta, Bhaskar, 2023. "Attack and interception in networks," Theoretical Economics, Econometric Society, vol. 18(4), November.
    9. Brian Lunday & Hanif Sherali, 2012. "Network interdiction to minimize the maximum probability of evasion with synergy between applied resources," Annals of Operations Research, Springer, vol. 196(1), pages 411-442, July.
    10. Sunghoon Hong & Myrna Wooders, 2010. "Strategic Network Interdiction," Vanderbilt University Department of Economics Working Papers 1010, Vanderbilt University Department of Economics.
    11. Guzmán, Cristóbal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2022. "A sequential Stackelberg game for dynamic inspection problems," European Journal of Operational Research, Elsevier, vol. 302(2), pages 727-739.
    12. Dhruva Kartik & Ashutosh Nayyar, 2021. "Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 11(2), pages 363-388, June.
    13. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2016. "Hub Interdiction & Hub Protection problems: Model formulations & Exact Solution methods. (Revised)," IIMA Working Papers WP2016-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    14. Bakker, Craig & Webster, Jennifer B. & Nowak, Kathleen E. & Chatterjee, Samrat & Perkins, Casey J. & Brigantic, Robert, 2020. "Multi-Game Modeling for Counter-Smuggling," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    15. Shen, Yeming & Sharkey, Thomas C. & Szymanski, Boleslaw K. & Wallace, William (Al), 2021. "Interdicting interdependent contraband smuggling, money and money laundering networks," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    16. Matthews, Logan R. & Gounaris, Chrysanthos E. & Kevrekidis, Ioannis G., 2019. "Designing networks with resiliency to edge failures using two-stage robust optimization," European Journal of Operational Research, Elsevier, vol. 279(3), pages 704-720.
    17. Alpern, Steve & Fokkink, Robbert & Simanjuntak, Martin, 2016. "Optimal search and ambush for a hider who can escape the search region," European Journal of Operational Research, Elsevier, vol. 251(3), pages 707-714.
    18. Kvasov, Dmitriy, 2015. "From Sabotage Games to Border Protection," CEI Working Paper Series 2015-2, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
    19. Tayyebi, Javad & Mitra, Ankan & Sefair, Jorge A., 2023. "The continuous maximum capacity path interdiction problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 38-52.
    20. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.

    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:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0366-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.