IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v47y2024i4d10.1007_s10878-024-01163-5.html
   My bibliography  Save this article

Constrained heterogeneous two-facility location games with sum-variant

Author

Listed:
  • Qi Zhao

    (Ocean University of China)

  • Wenjing Liu

    (Ocean University of China)

  • Qingqin Nong

    (Ocean University of China)

  • Qizhi Fang

    (Ocean University of China)

Abstract

We study deterministic mechanism design for constrained heterogeneous two-facility location games. The constraint here means that the feasible locations of facilities are specified and the number of facilities that can be built at each feasible location is limited. Given that a set of agents can strategically report their locations on the real line, the authority wants to design strategyproof mechanisms (i.e., mechanisms that can incentivize agents to report truthful private information) to construct two heterogeneous facilities under constraint, while optimizing the corresponding social objectives. Assuming that each agent’s individual objective depends on the sum of her distance to facilities, we consider locating desirable and obnoxious facilities respectively. For the former, we give a deterministic group strategyproof mechanism, which guarantees 3-approximation under the objectives of minimizing the sum cost and the maximum cost. We show that no deterministic strategyproof mechanism can have an approximation ratio of less than 2 under the sum/maximum cost objective. For the latter, we give a deterministic group strategyproof mechanism with 2-approximation under the objectives of maximizing the sum utility and the minimum utility. We show that no deterministic strategyproof mechanism can have an approximation ratio of less than 3/2 under the sum utility objective and 2 under the minimum utility objective, respectively.

Suggested Citation

  • Qi Zhao & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2024. "Constrained heterogeneous two-facility location games with sum-variant," Journal of Combinatorial Optimization, Springer, vol. 47(4), pages 1-21, May.
  • Handle: RePEc:spr:jcomop:v:47:y:2024:i:4:d:10.1007_s10878-024-01163-5
    DOI: 10.1007/s10878-024-01163-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-024-01163-5
    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/s10878-024-01163-5?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. Qiang Zhang & Minming Li, 2014. "Strategyproof mechanism design for facility location games with weighted agents on a line," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 756-773, November.
    2. Xin Chen & Qizhi Fang & Wenjing Liu & Yuan Ding & Qingqin Nong, 2022. "Strategyproof mechanisms for 2-facility location games with minimax envy," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1628-1644, July.
    3. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    4. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    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. Qi Zhao & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2023. "Constrained heterogeneous facility location games with max-variant cost," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-20, April.
    2. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 287-309, August.
    3. Lili Mei & Deshi Ye & Yong Zhang, 2018. "Approximation strategy-proof mechanisms for obnoxious facility location on a line," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 549-571, August.
    4. repec:spo:wpmain:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    5. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    7. Sidartha Gordon, 2015. "Unanimity in attribute-based preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 13-29, January.
    8. Bossert, Walter & Sprumont, Yves, 2014. "Strategy-proof preference aggregation: Possibilities and characterizations," Games and Economic Behavior, Elsevier, vol. 85(C), pages 109-126.
    9. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    10. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    11. Mihir Bhattacharya & Ojasvi Khare, 2024. "Strategy-proof interval-social choice correspondences over extended single-peaked domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 893-911, September.
    12. Sidartha Gordon, 2014. "Unanimity in Attribute-Based Preference Domains," SciencePo Working papers Main hal-01061994, HAL.
    13. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics, revised Apr 2025.
    14. repec:spo:wpecon:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    15. Masashi Umezawa, 2012. "The replacement principle for the provision of multiple public goods on tree networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 211-235, February.
    16. Takashi Kurihara & Koichi Suga, 2020. "Decision–making on public facility location by using social choice rules with a deliberative suggestion," Working Papers 1924, Waseda University, Faculty of Political Science and Economics.
    17. Madhuparna Karmokar & Souvik Roy & Ton Storcken, 2021. "Necessary and sufficient conditions for pairwise majority decisions on path-connected domains," Theory and Decision, Springer, vol. 91(3), pages 313-336, October.
    18. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    19. Ehlers, Lars, 2001. "Independence axioms for the provision of multiple public goods as options," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 239-250, March.
    20. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    21. Jordi Massó & Shurojit Chatterji, 2015. "On Strategy-proofness and the Salience of Single-peakedness," UFAE and IAE Working Papers 952.15, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    22. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.

    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:47:y:2024:i:4:d:10.1007_s10878-024-01163-5. 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.