IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/vyid10.1007_s10878-020-00556-6.html
   My bibliography  Save this article

Tighter price of anarchy for selfish task allocation on selfish machines

Author

Listed:
  • Xiayan Cheng

    (Hunan Normal University
    Hunan First Normal University)

  • Rongheng Li

    (Hunan Normal University)

  • Yunxia Zhou

    (Hunan Normal University)

Abstract

Given a set $$L = \{J_1,J_2,\ldots ,J_n\}$$L={J1,J2,…,Jn} of n tasks and a set $$M = \{M_1,M_2, \ldots ,M_m\}$$M={M1,M2,…,Mm} of m identical machines, in which tasks and machines are possessed by different selfish clients. Each selfish client of machine $$M_i \in M$$Mi∈M gets a profit equal to its load and each selfish client of task allocated to $$M_i$$Mi suffers from a cost equal to the load of $$M_i$$Mi. Our aim is to allocate the tasks on the m machines so as to minimize the maximum completion times of the tasks on each machine. A stable allocation is referred to as a dual equilibrium (DE). We firstly show that 4/3 is tight upper bound of the Price of Anarchy(PoA) with respect to dual equilibrium for $$m\in \{3,\ldots ,9\}$$m∈{3,…,9}. And secondly $$(7m-6)/(5m-3)$$(7m-6)/(5m-3) is an upper bound for $$m\ge 10$$m≥10. The result is better than the existing bound of 7/5.

Suggested Citation

  • Xiayan Cheng & Rongheng Li & Yunxia Zhou, 0. "Tighter price of anarchy for selfish task allocation on selfish machines," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-32.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00556-6
    DOI: 10.1007/s10878-020-00556-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00556-6
    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/s10878-020-00556-6?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. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    2. Hui-Chih Hung & Bertrand M. T. Lin & Marc E. Posner & Jun-Min Wei, 2019. "Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs," Journal of Scheduling, Springer, vol. 22(4), pages 413-431, August.
    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. Xiayan Cheng & Rongheng Li & Yunxia Zhou, 2022. "Tighter price of anarchy for selfish task allocation on selfish machines," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1848-1879, October.
    2. Levin, Hagay & Schapira, Michael & Zohar, Aviv, 2006. "The Strategic Justification for BGP," MPRA Paper 2110, University Library of Munich, Germany.
    3. Shahar Dobzinski & Noam Nisan & Michael Schapira, 2005. "Truthful Randomized Mechanisms for Combinatorial Auctions," Discussion Paper Series dp408, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Matan Atsmony & Gur Mosheiov, 2023. "Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection," Journal of Scheduling, Springer, vol. 26(2), pages 193-207, April.
    5. M. Y. Jumba & Y. S. Haruna & U. O. Aliyu & A. L. Amao, 2024. "Application of Games Theory in Modelling of Nigerian Electricity Market," International Journal of Research and Scientific Innovation, International Journal of Research and Scientific Innovation (IJRSI), vol. 11(5), pages 1129-1140, May.
    6. Babaioff, Moshe & Nisan, Noam & Pavlov, Elan, 2009. "Mechanisms for a spatially distributed market," Games and Economic Behavior, Elsevier, vol. 66(2), pages 660-684, July.
    7. Aziz, Haris & Chan, Hau & Lee, Barton E. & Parkes, David C., 2020. "The capacity constrained facility location problem," Games and Economic Behavior, Elsevier, vol. 124(C), pages 478-490.
    8. Rachel R. Chen & Robin O. Roundy & Rachel Q. Zhang & Ganesh Janakiraman, 2005. "Efficient Auction Mechanisms for Supply Chain Procurement," Management Science, INFORMS, vol. 51(3), pages 467-482, March.
    9. Zhiling Guo & Gary J. Koehler & Andrew B. Whinston, 2012. "A Computational Analysis of Bundle Trading Markets Design for Distributed Resource Allocation," Information Systems Research, INFORMS, vol. 23(3-part-1), pages 823-843, September.
    10. Kimmo Berg & Harri Ehtamo, 2012. "Continuous learning methods in two-buyer pricing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 287-304, June.
    11. Itai Ashlagi & Shahar Dobzinski & Ron Lavi, 2012. "Optimal Lower Bounds for Anonymous Scheduling Mechanisms," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 244-258, May.
    12. Yuval Emek & Michal Feldman, 2007. "Computing an Optimal Contract in Simple Technologies," Discussion Paper Series dp452, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. Parikshit De & Manipushpak Mitra, 2017. "Incentives and justice for sequencing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 239-264, August.
    14. Bhavook Bhardwaj & Siddharth Chatterjee, 2022. "Decisions over Sequences," Papers 2203.00070, arXiv.org, revised Sep 2022.
    15. Benjamin Blau & Clemens Dinther & Tobias Conte & Yongchun Xu & Christof Weinhardt, 2009. "How to Coordinate Value Generation in Service Networks," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 1(5), pages 343-356, October.
    16. Mu'alem, Ahuva, 2014. "Fair by design: Multidimensional envy-free mechanisms," Games and Economic Behavior, Elsevier, vol. 88(C), pages 29-46.
    17. Wada, Kentaro & Akamatsu, Takashi, 2013. "A hybrid implementation mechanism of tradable network permits system which obviates path enumeration: An auction mechanism with day-to-day capacity control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 94-112.
    18. Antonio Fernández Anta & Chryssis Georgiou & Miguel A Mosteiro & Daniel Pareja, 2015. "Algorithmic Mechanisms for Reliable Crowdsourcing Computation under Collusion," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-22, March.
    19. Babaioff, Moshe & Blumrosen, Liad, 2008. "Computationally-feasible truthful auctions for convex bundles," Games and Economic Behavior, Elsevier, vol. 63(2), pages 588-620, July.
    20. Paul Gölz & Dominik Peters & Ariel Procaccia, 2022. "In This Apportionment Lottery, the House Always Wins," Post-Print hal-03834513, HAL.

    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::y::i::d:10.1007_s10878-020-00556-6. 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.