IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v207y2013i1p181-20010.1007-s10479-011-1057-2.html
   My bibliography  Save this article

Strategies in competing subset selection

Author

Listed:
  • Claudia Marini
  • Gaia Nicosia
  • Andrea Pacifici
  • Ulrich Pferschy

Abstract

We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential procedure consisting in a fixed number of rounds. In every round each agent submits one item that may be included in its solution set. We study two natural rules to decide which item between the two will be included. We address the problem from a strategic point of view, that is finding the best moves for one agent against the opponent, in two distinct scenarios. We consider preventive or minimax strategies, optimizing the objective of the agent in the worst case, and best-response strategies, where the items submitted by the opponent are known in advance in each round. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Claudia Marini & Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy, 2013. "Strategies in competing subset selection," Annals of Operations Research, Springer, vol. 207(1), pages 181-200, August.
    • Handle: RePEc:spr:annopr:v:207:y:2013:i:1:p:181-200:10.1007/s10479-011-1057-2
    DOI: 10.1007/s10479-011-1057-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-1057-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-1057-2?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. Schlag, Karl H. & Sela, Aner, 1998. "You play (an action) only once," Economics Letters, Elsevier, vol. 59(3), pages 299-303, June.
    2. Kahn, J & Lagarias, J C & Witsenhausen, H S, 1987. "Single-Suit Two-Person Card Play," International Journal of Game Theory, Springer;Game Theory Society, vol. 16(4), pages 291-320.
    3. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    4. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    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. Darmann, Andreas & Nicosia, Gaia & Pferschy, Ulrich & Schauer, Joachim, 2014. "The Subset Sum game," European Journal of Operational Research, Elsevier, vol. 233(3), pages 539-549.
    2. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy, 2018. "Competitive multi-agent scheduling with an iterative selection rule," 4OR, Springer, vol. 16(1), pages 15-29, March.

    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. Nong, Q.Q. & Cheng, T.C.E. & Ng, C.T., 2011. "Two-agent scheduling to minimize the total cost," European Journal of Operational Research, Elsevier, vol. 215(1), pages 39-44, November.
    2. Byung-Cheon Choi & Myoung-Ju Park, 2016. "An Ordered Flow Shop with Two Agents," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-24, October.
    3. Shesh Narayan Sahu & Yuvraj Gajpal & Swapan Debbarma, 2018. "Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives," Annals of Operations Research, Springer, vol. 269(1), pages 623-640, October.
    4. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    5. Ruyan He & Jinjiang Yuan, 2020. "Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    6. Koulamas, Christos, 2015. "A note on scheduling problems with competing agents and earliness minimization objectives," European Journal of Operational Research, Elsevier, vol. 245(3), pages 875-876.
    7. Ren-Xia Chen & Shi-Sheng Li, 2019. "Two-agent single-machine scheduling with cumulative deterioration," 4OR, Springer, vol. 17(2), pages 201-219, June.
    8. Hao Yan & Peihai Liu & Xiwen Lu, 2023. "Vehicle scheduling problems with two agents on a line," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-18, January.
    9. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    10. Xiaoqiang Cai & George L. Vairaktarakis, 2012. "Coordination of Outsourced Operations at a Third-Party Facility Subject to Booking, Overtime, and Tardiness Costs," Operations Research, INFORMS, vol. 60(6), pages 1436-1450, December.
    11. Jun Pei & Jinling Wei & Baoyu Liao & Xinbao Liu & Panos M. Pardalos, 2020. "Two-agent scheduling on bounded parallel-batching machines with an aging effect of job-position-dependent," Annals of Operations Research, Springer, vol. 294(1), pages 191-223, November.
    12. Wan, Guohua & Vakati, Sudheer R. & Leung, Joseph Y.-T. & Pinedo, Michael, 2010. "Scheduling two agents with controllable processing times," European Journal of Operational Research, Elsevier, vol. 205(3), pages 528-539, September.
    13. Dan A. Iancu & Nikolaos Trichakis, 2014. "Pareto Efficiency in Robust Optimization," Management Science, INFORMS, vol. 60(1), pages 130-147, January.
    14. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy & Julia Resch & Giovanni Righini, 2021. "Optimally rescheduling jobs with a Last-In-First-Out buffer," Journal of Scheduling, Springer, vol. 24(6), pages 663-680, December.
    15. Tang, Lixin & Zhao, Xiaoli & Liu, Jiyin & Leung, Joseph Y.-T., 2017. "Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine," European Journal of Operational Research, Elsevier, vol. 263(2), pages 401-411.
    16. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    17. Gao, Yuan & Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2019. "A further study on two-agent parallel-batch scheduling with release dates and deteriorating jobs to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 273(1), pages 74-81.
    18. Shang-Chia Liu & Jiahui Duan & Win-Chin Lin & Wen-Hsiang Wu & Jan-Yee Kung & Hau Chen & Chin-Chia Wu, 2018. "A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    19. Darmann, Andreas & Nicosia, Gaia & Pferschy, Ulrich & Schauer, Joachim, 2014. "The Subset Sum game," European Journal of Operational Research, Elsevier, vol. 233(3), pages 539-549.
    20. Kejun Zhao & Xiwen Lu & Manzhan Gu, 2016. "A new approximation algorithm for multi-agent scheduling to minimize makespan on two machines," Journal of Scheduling, Springer, vol. 19(1), pages 21-31, 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:annopr:v:207:y:2013:i:1:p:181-200:10.1007/s10479-011-1057-2. 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.