Winner-imposing strategyproof mechanisms for multiple Facility Location games

We study Facility Location games, where a number of facilities are placed in a metric space based on locations reported by strategic agents. A mechanism maps the agents' locations to a set of facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in mechanisms that are strategyproof, i.e., ensure that no agent can benefit frommisreporting her location, do not resort to monetary transfers, and approximate the optimal social cost. We focus on the closely related problems of k-Facility Location and Facility Location with a uniform facility opening cost, and mostly study winner-imposing mechanisms, which allocate facilities to the agents and require that each agent allocated a facility should connect to it. We show that the winner-imposing version of the Proportional Mechanism (Lu et al., EC '10) is stategyproof and 4k-approximate for the k-Facility Location game. For the Facility Location game, we show that the winner-imposing version of the randomized algorithm of (Meyerson, FOCS '01), which has an approximation ratio of 8, is strategyproof. Furthermore, we present a deterministic non-imposing group strategyproof O(log n)-approximate mechanism for the Facility Location game on the line.

[1]  Biung-Ghi Ju,et al.  Efficiency and consistency for locating multiple public facilities , 2008, J. Econ. Theory.

[2]  H. Moulin.  On strategy-proofness and single peakedness , 1980 .

[3]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[4]  Salvador Barberà,et al.  An introduction to strategy-proof social choice functions , 2001, Soc. Choice Welf..

[5]  Eiichi Miyagawa,et al.  Locating libraries on a street , 2001, Soc. Choice Welf..

[6]  Kunal Talwar,et al.  Mechanism Design via Differential Privacy , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[7]  Faruk Gul,et al.  Generalized Median Voter Schemes and Committees , 1993 .

[8]  Zeyuan Allen Zhu,et al.  Asymptotically optimal strategy-proof mechanisms for two-facility games , 2010, EC '10.

[9]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[10]  Aaron Roth,et al.  Differentially private combinatorial optimization , 2009, SODA '10.

[11]  Moshe Tennenholtz,et al.  Approximately optimal mechanism design via differential privacy , 2010, ITCS '12.

[12]  Said Salhi,et al.  Discrete Location Theory , 1991 .

[13]  Sudipto Guha,et al.  Approximation algorithms for facility location problems , 2000 .

[14]  Yuan Zhou,et al.  Tighter Bounds for Facility Games , 2009, WINE.

[15]  Moshe Tennenholtz,et al.  Approximate mechanism design without money , 2009, EC '09.

[16]  Yves Sprumont.  The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule , 1991 .

[17]  Salvador Barberà,et al.  Locating public facilities by majority: Stability, consistency and group formation , 2006, Games Econ. Behav..

[18]  M. Jackson,et al.  A characterization of strategy-proof social choice functions for economies with pure public goods , 1994 .

[19]  Russell Bent,et al.  A simple and deterministic competitive algorithm for online facility location , 2004, Inf. Comput..

[20]  Yves Sprumont.  Strategyproof Collective Choice in Economic and Political Environments , 1995 .

[21]  Noga Alon,et al.  Strategyproof Approximation of the Minimax on Networks , 2010, Math. Oper. Res..

[22]  David B. Shmoys,et al.  Approximation algorithms for facility location problems , 2000, APPROX.

[23]  Adam Meyerson,et al.  Online facility location , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[24]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[25]  Daniel A. Spielman,et al.  Spectral Graph Theory and its Applications , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[26]  Rakesh V. Vohra,et al.  Strategy-proof Location on a Network , 2002, J. Econ. Theory.