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Two-facility-location games with mixed types of agents

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  • Gai, Ling
  • Liang, Mengpei
  • Wang, Chenhao

Abstract

This paper examines the mechanism design for a two-facility-location game involving two types of agents. Type I agents only prioritize the facility closer to their location, while type II agents are concerned with the overall distance to both facilities. The objective is to minimize the total cost of all agents. In a game setting, agents have the option to strategically report their locations or types. Therefore, a mechanism which ensures that agents do not have any incentive to misreport their private information is considered strategy-proof. We design strategy-proof mechanisms with approximation ratios for both continuous and discrete facility locations, which are designed with respect to various restrictions on misreporting. Furthermore, we establish lower bounds on approximation ratios.

Suggested Citation

  • Gai, Ling & Liang, Mengpei & Wang, Chenhao, 2024. "Two-facility-location games with mixed types of agents," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006483
    DOI: 10.1016/j.amc.2023.128479
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    References listed on IDEAS

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    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. Monabbati, Ehsan & Kakhki, Hossein Taghizadeh, 2015. "On a class of subadditive duals for the uncapacitated facility location problem," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 118-131.
    3. Jian, Qing & Li, Xiaopeng & Wang, Juan & Xia, Chengyi, 2021. "Impact of reputation assortment on tag-mediated altruistic behaviors in the spatial lattice," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. 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.
    5. Deligkas, Argyrios & Filos-Ratsikas, Aris & Voudouris, Alexandros A., 2023. "Heterogeneous facility location with limited resources," Games and Economic Behavior, Elsevier, vol. 139(C), pages 200-215.
    6. Chen, Yanbin & Li, Sanxi & Lin, Kai & Yu, Jun, 2021. "Consumer search with blind buying," Games and Economic Behavior, Elsevier, vol. 126(C), pages 402-427.
    7. Gao, Hongyu & Wang, Juan & Zhang, Fan & Li, Xiaopeng & Xia, Chengyi, 2021. "Cooperation dynamics based on reputation in the mixed population with two species of strategists," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    8. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
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