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A Survey on Approximation Mechanism Design Without Money for Facility Games

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Advances in Global Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 95))

Abstract

In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games.

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Acknowledgements

Research was partially supported by the Nature Science Foundation of China (No. 11301475) and the Nature Science Foundation of Zhejiang Province, China (No. LQ12A01011).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Yukun Cheng

  2. Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

    Sanming Zhou

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  1. Yukun Cheng
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  2. Sanming Zhou
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Correspondence to Yukun Cheng .

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Editors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University Australia, Ballarat, Victoria, Australia

    David Gao

  2. School Science, Inform., Tech. & Engg., Federation University Australia, Ballarat, Victoria, Australia

    Ning Ruan

  3. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Wenxun Xing

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Cheng, Y., Zhou, S. (2015). A Survey on Approximation Mechanism Design Without Money for Facility Games. In: Gao, D., Ruan, N., Xing, W. (eds) Advances in Global Optimization. Springer Proceedings in Mathematics & Statistics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-08377-3_13

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