Non-cooperative Facility Location and Covering Games

Proceedings of the 4th ACM conference on Electronic commerce - EC '03, 2003

Strategyproof cost-sharing mechanisms, lying in the core, that recover 1/a fraction of the cost, are presented for the set cover and facility location games: a=O(log n) for the former and 1:861 for the latter. Our mechanisms utilize approximation algorithms for these problems based on the method of dual-fitting. D

In a non-cooperative game, a Nash equilibrium corresponds to a set of strategies, which ensure that none of the players are better off by unilaterally changing his strategy. This work focuses on the application of Nash Equilibrium to the competitive facility location. Its aim is to provide an up to date review of the literature concerning the discrete version of the problem. He has eight books published by international houses and edited several special issues of international scientific journals. He has published more than 70 research papers and chapters in international scientific journals and scientific collections. His primary research interests are in mathematical programming, in the design and implementation of high performance computational algorithms and in their applications to decision problems that arise in large scale networks, in supply chain management and logistics.

2010

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 from misreporting 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(logn)-approximate mechanism for the Facility Location game on the line.

Revista de Informática Teórica e Aplicada, 2017

Resumo: O problema de Localização da Instalações é um problema de otimização combinatória NP-Difícil bem conhecido na literatura. Ele modela uma gama de situações onde se pretende fornecer um conjunto de bens ou serviços através de um conjunto de instalações F para um conjunto de clientes T, também denominados terminais. Há custos de abertura para cada instalação em F e custos de conexão para cada par de instalações e clientes (f,t), onde a instalação f atende o cliente t.

2021

We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to her spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting times for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perf...

Optimization Letters, 2011

A continuous single-facility location problem, where the fixed cost (or installation cost) depends on the region where the new facility is located, is studied by mean of cooperative Game Theory tools. Core solutions are proposed for the total cost allocation problem. Sufficient conditions in order to have a nonempty core are given, then the Weber problem with regional fixed costs is studied.

European Journal of Operational Research, 2011

In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service radius of the coalition. We study the existence of core allocations and the existence of polynomial representations of the cores of these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths, and on the ℓ p metric spaces defined over R d .

Operations Research Letters, 2007

A noncooperative game theoretical approach is considered for the multifacility location problem. It turns out that the facility location game is a potential game in the sense of Monderer and Shapley and some properties of the game are studied.

2018

ECAI 2014

The study of facility location in the presence of selfinterested agents has recently emerged as the benchmark problem in the research on mechanism design without money. Here we study the related problem of heterogeneous 2-facility location, that features more realistic assumptions such as: (i) multiple heterogeneous facilities have to be located, (ii) agents' locations are common knowledge and (iii) agents bid for the set of facilities they are interested in. We study the approximation ratio of both deterministic and randomized truthful algorithms when the underlying network is a line. We devise an (n − 1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm.