Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMechanism Design for Facility Location Problems: A Survey
111
0
0.0
(
0
)
Added by
Chenhao Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The study of approximate mechanism design for facility location problems has been in the center of research at the intersection of artificial intelligence and economics for the last decades, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to design mechanisms to select a set of locations on which to build a set of facilities, aiming to optimize some social objective and ensure desirable properties based on the preferences of strategic agents, who might have incentives to misreport their private information such as their locations. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting the different variants and methodologies, as well as the most interesting directions for future research.
rate research
Read More
We study the facility location games with candidate locations from a mechanism design perspective. Suppose there are n agents located in a metric space whose locations are their private information, and a group of candidate locations for building facilities. The authority plans to build some homogeneous facilities among these candidates to serve the agents, who bears a cost equal to the distance to the closest facility. The goal is to design mechanisms for minimizing the total/maximum cost among the agents. For the single-facility problem under the maximum-cost objective, we give a deterministic 3-approximation group strategy-proof mechanism, and prove that no deterministic (or randomized) strategy-proof mechanism can have an approximation ratio better than 3 (or 2). For the two-facility problem on a line, we give an anonymous deterministic group strategy-proof mechanism that is (2n-3)-approximation for the total-cost objective, and 3-approximation for the maximum-cost objective. We also provide (asymptotically) tight lower bounds on the approximation ratio.
This paper is devoted to the two-opposite-facility location games with a penalty whose amount depends on the distance between the two facilities to be opened by an authority. The two facilities are opposite in that one is popular and the other is obnoxious. Every selfish agent in the game wishes to stay close to the popular facility and stay away from the obnoxious one; its utility is measured by the difference between its distances to the obnoxious facility and the popular one. The authority determines the locations of the two facilities on a line segment where all agents are located. Each agent has its location information as private, and is required to report its location to the authority. Using the reported agent locations as input, an algorithmic mechanism run by the authority outputs the locations of the two facilities with an aim to maximize certain social welfare. The sum-type social welfare concerns with the penalized total utility of all agents, for which we design both randomized and deterministic group strategy-proof mechanisms with provable approximation ratios, and establish a lower bound on the approximation ratio of any deterministic strategy-proof mechanism. The bottleneck-type social welfare concerns with the penalized minimum utility among all agents, for which we propose a deterministic group strategy-proof mechanism that ensures optimality.
In the standard Mechanism Design framework, agents messages are gathered at a central point and allocation/tax functions are calculated in a centralized manner, i.e., as functions of all network agents messages. This requirement may cause communication and computation overhead and necessitates the design of mechanisms that alleviate this bottleneck. We consider a scenario where message transmission can only be performed locally so that the mechanism allocation/tax functions can be calculated in a decentralized manner. Each agent transmits messages to her local neighborhood, as defined by a given message-exchange network, and her allocation/tax functions are only functions of the available neighborhood messages. This scenario gives rise to a novel research problem that we call Distributed Mechanism Design. In this paper, we propose two distributed mechanisms for network utility maximization problems that involve private and public goods with competition and cooperation between agents. As a concrete example, we use the problems of rate allocation in networks with either unicast or multirate multicast transmission protocols. The proposed mechanism for each of the protocols fully implements the optimal allocation in Nash equilibria and its message space dimensionality scales linearly with respect to the number of agents in the network.
We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces. The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanisms output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility. We overcome this barrier by employing and generalizing the computational model in the literature on $textit{Bernoulli factories}$. In a Bernoulli factory problem, one is given a function mapping the bias of an input coin to that of an output coin, and the challenge is to efficiently simulate the output coin given only sample access to the input coin. This is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of Hartline et al. (2015) exactly incentive compatible.
We consider a new setting of facility location games with ordinal preferences. In such a setting, we have a set of agents and a set of facilities. Each agent is located on a line and has an ordinal preference over the facilities. Our goal is to design strategyproof mechanisms that elicit truthful information (preferences and/or locations) from the agents and locate the facilities to minimize both maximum and total cost objectives as well as to maximize both minimum and total utility objectives. For the four possible objectives, we consider the 2-facility settings in which only preferences are private, or locations are private. For each possible combination of the objectives and settings, we provide lower and upper bounds on the approximation ratios of strategyproof mechanisms, which are asymptotically tight up to a constant. Finally, we discuss the generalization of our results beyond two facilities and when the agents can misreport both locations and preferences.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
