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Register a new userMechanism Design for Two-Opposite-Facility Location Games with Penalties on Distance
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Added by
Zhongzheng Tang
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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.
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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.
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.
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.
Recommendation systems are extremely popular tools for matching users and contents. However, when content providers are strategic, the basic principle of matching users to the closest content, where both users and contents are modeled as points in some semantic space, may yield low social welfare. This is due to the fact that content providers are strategic and optimize their offered content to be recommended to as many users as possible. Motivated by modern applications, we propose the widely studied framework of facility location games to study recommendation systems with strategic content providers. Our conceptual contribution is the introduction of a $textit{mediator}$ to facility location models, in the pursuit of better social welfare. We aim at designing mediators that a) induce a game with high social welfare in equilibrium, and b) intervene as little as possible. In service of the latter, we introduce the notion of $textit{intervention cost}$, which quantifies how much damage a mediator may cause to the social welfare when an off-equilibrium profile is adopted. As a case study in high-welfare low-intervention mediator design, we consider the one-dimensional segment as the user domain. We propose a mediator that implements the socially optimal strategy profile as the unique equilibrium profile, and show a tight bound on its intervention cost. Ultimately, we consider some extensions, and highlight open questions for the general agenda.
We address the problem of strategyproof (SP) facility location mechanisms on discrete trees. Our main result is a full characterization of onto and SP mechanisms. In particular, we prove that when a single agent significantly affects the outcome, the trajectory of the facility is almost contained in the trajectory of the agent, and both move in the same direction along the common edges. We show tight relations of our characterization to previous results on discrete lines and on continuous trees. We then derive further implications of the main result for infinite discrete lines.
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