A Survey on Approximation Mechanism Design without Money for Facility Games

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

Proportional Fairness and Strategic Behaviour in Facility Location Problems

The one-dimensional facility location problem readily generalizes to many real world problems, including social choice, project funding, and the geographic placement of facilities intended to serve a set of agents. In these problems, each agent has a preferred point along a line or interval, which could denote their ideal preference, preferred project funding, or location. Thus each agent wishes the facility to be as close to their preferred point as possible. We are tasked with designing a mechanism which takes in these preferred points as input, and outputs an ideal location to build the facility along the line or interval domain. In addition to minimizing the distance between the facility and the agents, we may seek a facility placement which is fair for the agents. In particular, this thesis focusses on the notion of proportional fairness, in which endogenous groups of agents with similar or identical preferences have a distance guarantee from the facility that is proportional to the size of the group. We also seek mechanisms that are strategyproof, in that no agent can improve their distance from the facility by lying about their location. We consider both deterministic and randomized mechanisms, in both the classic and obnoxious facility location settings. The obnoxious setting differs from the classic setting in that agents wish to be far from the facility rather than close to it. For these settings, we formalize a hierarchy of proportional fairness axioms, and where possible, characterize strategyproof mechanisms which satisfy these axioms. In the obnoxious setting where this is not possible, we consider the welfare-optimal mechanisms which satisfy these axioms, and quantify the extent at which the system efficiency is compromised by misreporting agents. We also investigate, in the classic setting, the nature of misreporting agents under a family of proportionally fair mechanisms which are not necessarily strategyproof. These results are supplemented with tight approximation ratio and price of fairness bounds which provide further insight into the compromise between proportional fairness and efficiency in the facility location problem. Finally, we prove basic existence results concerning possible extensions to our settings

Public Facility Location: Issues and Approaches

The papers collected in this issue were presented at the Task Force Meeting on Public Facility Location, held at IIASA in June 1980. The meeting was an important occasion for scientists with different backgrounds and nationalities to compare and discuss differences and similarities among their approaches to location problems. Unification and reconciliation of existing theories and methods was one of the leading themes of the meeting, and the papers collected here are part of the raw material to be used as a starting point towards this aim. The papers themselves provide a wide spectrum of approaches to both technical and substantive problems, for example, the way space is treated (continuously in Beckmann, in Mayhew, and in Thisse et al, discretely in all the others), the way customers are assigned to facilities (by behavioral models in Ermoliev and Leonardi, in Sheppard, and in Wilson, by normative rules in many others), the way the objective function is defined (ranging from total cost, to total profit, total expected utility for customers, accessibility, minimax distance, maximum covering, to a multi-objective treatment of all of them as in Revelle et al. There is indeed room for discussion, in order to find both similarities and weaknesses in different approaches. A general weakness of the current state of the art of location modeling may also be recognized: its general lack of realism relative to the political and institutional issues implied by locational decisions. This criticism, developed by Lea, might be used both as a concluding remark and as a proposal for new challenging research themes to scholars working in the field of location theory