Strategyproof facility location with concave costs

Fotakis, Dimitris; Tzamos, Christos

doi:10.1145/2692359.2692370

Cited by 4 publications

(7 citation statements)

References 27 publications

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“…Specifically, Escoffier et al [2011] had proven that in this case, the INVERSELY PROPORTIONAL mechanism is strategyproof and approximates the optimal total connection cost within a factor of (K + 1)/2 for K-Facility Location in general metric spaces. In Fotakis and Tzamos [2013a], we present a randomized strategyproof mechanism that applies to instances with K facilities and K + 1 agents on the line and is 2-approximate for the objective of total cost, thus improving on the approximation ratio of (K + 1)/2 obtained in Escoffier et al [2011]. Notably, Theorem 3.7 shows that instances with only K + 1 agents are hard for deterministic mechanisms.…”

Section: Other Related Workmentioning

confidence: 99%

“…Locating Multiple Facilities. Very recently, we presented, in Fotakis and Tzamos [2013a], the first randomized strategyproof mechanism with a bounded approximation ratio for K-Facility Location on the line. The mechanism works by equalizing the expected connection cost of all agents, and is n-approximate for the total connection cost and 2-approximate for the maximum connection cost of the agents.…”

Section: Other Related Workmentioning

confidence: 99%

“…Prior to Fotakis and Tzamos [2013a], for K ≥ 4, the case of K + 1 agents was the only one where a (randomized) strategyproof mechanism with a bounded approximation ratio had been known. Specifically, Escoffier et al [2011] had proven that in this case, the INVERSELY PROPORTIONAL mechanism is strategyproof and approximates the optimal total connection cost within a factor of (K + 1)/2 for K-Facility Location in general metric spaces.…”

Section: Other Related Workmentioning

confidence: 99%

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On the Power of Deterministic Mechanisms for Facility Location Games

Fotakis

Tzamos

2014

ACM Trans. Econ. Comput.

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106

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We consider K-Facility Location games, where n strategic agents report their locations in a metric space and a mechanism maps them to K 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 deterministic mechanisms that are strategyproof, that is, ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and achieve a bounded approximation ratio to the total connection cost of the agents (or to the L p norm of the connection costs, for some p ∈ [1, ∞) or for p = ∞).Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. In particular, we show that for instances with n ≥ 5 agents, any such mechanism either admits a unique dictator or always places the facilities at the leftmost and the rightmost location of the instance. As a corollary, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for the problem of locating 2 facilities on the line to minimize the total connection cost is precisely n− 2. Another rather surprising consequence is that the TWO-EXTREMES mechanism of Procaccia and Tennenholtz [2009] is the only deterministic anonymous strategyproof mechanism with a bounded approximation ratio for 2-Facility Location on the line.The proof of the characterization employs several new ideas and technical tools, which provide new insights into the behavior of deterministic strategyproof mechanisms for K-Facility Location games and may be of independent interest. Employing one of these tools, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K-Facility Location on the line, even for simple instances with K + 1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location and instances with n ≥ 3 agents located in a star. ACM Reference Format:Dimitris Fotakis and Christos Tzamos. 2014. On the power of deterministic mechanisms for facility location games. ACM Trans. Econom.

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Section: Other Related Workmentioning

confidence: 99%

Section: Other Related Workmentioning

confidence: 99%

Section: Other Related Workmentioning

confidence: 99%

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On the Power of Deterministic Mechanisms for Facility Location Games

Fotakis

Tzamos

2014

ACM Trans. Econ. Comput.

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106

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“…Nevertheless, there have been only few examples of truthful mechanisms with good approximation guarantees that are not based on additional assumptions. All of them concern some simple and restricted domains (see for e.g., [1,12,22,27] for placing 1 or 2 facilities in a metric space and [26] for voting with positional scoring rules). For less restricted domains, there are strong lower bounds on the best possible approximation ratio achievable by truthful mechanisms (see e.g., [14] for deterministic facility location mechanisms).…”

Section: A1 Other Related Previous Workmentioning

confidence: 99%

“…As a proof of concept, we apply selective verification to k-Facility Location problems (Section 4), which have served as benchmarks in approximate mechanism design without money (see e.g., [27,1,22,12] and the references therein). We show that Greedy ([30, Section 2.2]) and Proportional [22] satisfy participation and are robust and truthful, if we verify the k agents allocated the facilities (Theorems 4.1 and 4.2).…”

Section: Introductionmentioning

confidence: 99%

Who to Trust for Truthfully Maximizing Welfare?

Fotakis,

Tzamos,

Zampetakis

2015

Preprint

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We introduce a general approach based on selective verification and obtain approximate mechanisms without money for maximizing the social welfare in the general domain of utilitarian voting. Having a good allocation in mind, a mechanism with verification selects few critical agents and detects, using a verification oracle, whether they have reported truthfully. If yes, the mechanism produces the desired allocation. Otherwise, the mechanism ignores any misreports and proceeds with the remaining agents. We obtain randomized truthful (or almost truthful) mechanisms without money that verify only O(ln m/ε) agents, where m is the number of outcomes, independently of the total number of agents, and are (1 − ε)-approximate for the social welfare. We also show that any truthful mechanism with a constant approximation ratio needs to verify Ω(log m) agents. A remarkable property of our mechanisms is robustness, namely that their outcome depends only on the reports of the truthful agents.

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The obnoxious facility location game with dichotomous preferences

Plaxton

Sinha

2023

Theoretical Computer Science

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Strategyproof facility location with concave costs

Cited by 4 publications

References 27 publications

On the Power of Deterministic Mechanisms for Facility Location Games

On the Power of Deterministic Mechanisms for Facility Location Games

Who to Trust for Truthfully Maximizing Welfare?

The obnoxious facility location game with dichotomous preferences

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