Non-Cooperative Facility Location Games: a Survey

The Facility Location problem is a well-know NP-Hard combinatorial optimization problem. It models a diverse set of situations where one aims to provide a set of goods or services via a set of facilities F to a set of clients T, also called terminals. There are opening costs for each facility in F and connection costs for each pair of facility and client, if such facility attends this client. A central authority wants to determine the solution with minimum cost, considering both opening and connection costs, in such a way that all clients are attended by one facility. In this survey we are interested in the non-cooperative game version of this problem, where instead of having a central authority, each client is a player and decides where to con- nect himself. In doing so, he aims to minimize his own costs, given by the connection costs and opening costs of the facility, which may be shared among clients using the same facility. This problem has several applications as well, specially in distributed scenarios where a central authority is too expensive or even infeasible to exist. In this paper we present a survey describing different variants of this problem and reviewing several results about it, as well as adapting results from existing literature concerning the existence of equilibria, Price of Anarchy and Price of Stability. We also point out open problems that remain to be addressed.

A cooperative location game based on the 1-center location problem

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 call these games the Minimum Radius Location Games (MRLG). 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 ¿ p metric spaces defined over R d. © 2011 Elsevier B.V. All rights reserved.The research of the authors is partially supported by Spanish grants MTM2007-67433, MTM2010-19576-C02-01 and Junta Andalucia/FEDER grant FQM-5849.Puerto Albandoz, J.; Tamir, A.; Perea Rojas Marcos, F. (2011). A cooperative location game based on the 1-center location problem. European Journal of Operational Research. 214(2):317-330. https://doi.org/10.1016/j.ejor.2011.04.020S317330214

Strategic Facility Location with Clients that Minimize Total Waiting Time

We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.Comment: To appear at the 37th AAAI Conference on Artificial Intelligence (AAAI-23), full versio

Cooperative provision of indivisible public goods.

A community faces the obligation of providing an indivisible public good. Each member is capable of providing it at a certain cost and the solution is to rely on the player who can do it at the lowest cost. It is then natural that he or she be compensated by the other players. The question is to know how much they should each contribute. We model this compensation problem as a cost sharing game to which standard allocation rules are applied and related to the solution resulting from the auction procedures proposed by Kleindorfer and Sertel (1994).public goods, cost sharing, core, nucleolus, Shapley value.

Coordination of Mobile Mules via Facility Location Strategies

In this paper, we study the problem of wireless sensor network (WSN) maintenance using mobile entities called mules. The mules are deployed in the area of the WSN in such a way that would minimize the time it takes them to reach a failed sensor and fix it. The mules must constantly optimize their collective deployment to account for occupied mules. The objective is to define the optimal deployment and task allocation strategy for the mules, so that the sensors' downtime and the mules' traveling distance are minimized. Our solutions are inspired by research in the field of computational geometry and the design of our algorithms is based on state of the art approximation algorithms for the classical problem of facility location. Our empirical results demonstrate how cooperation enhances the team's performance, and indicate that a combination of k-Median based deployment with closest-available task allocation provides the best results in terms of minimizing the sensors' downtime but is inefficient in terms of the mules' travel distance. A k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc

Face to Face Negotiation to Overcome the Nimby Syndrome: Theory and Experimental Design

In recent decade, community after community has refused to accept facilities that require large amounts of land and generate local environmental costs such as airports, trash disposal plants or waste incinerators. Faced with this problem economists have used several methods such as lotteries, auctions or insurance policies. However, all those mechanisms have theoretical shortcomings. Therefore, we propose an approach based on face to face negotiation between elected representative. In order to reduce transaction costs, we introduce an arbitrator that proposes surplus distribution and a host community. The main question in this paper is to determine which distribution it has to propose to quickly reach an agreement. To answer this question we revise the traditional structure of cooperative games and explore the predictive power of three generalized solutions by implementing laboratory bargaining experiments Lors de la localisation d’équipements générateurs de nuisances tels que les décharges ou les incinérateurs, la commune d’accueil subit l’ensemble des coûts tandis que les autres communes perçoivent des bénéfices. Ainsi, fréquemment, les riverains du projet s’opposent à l’implantation et les projets de localisation n’aboutissent pas. Confrontés à ce problème, les économistes ont utilisés de nombreuses méthodes telles que les loteries, les enchères ou les assurances. Cependant, tous ces mécanismes ne parviennent pas à réduire l’opposition des riverains. Par conséquent, nous proposons une approche basée sur une négociation face à face entre les représentants des communes. Dans le but de réduire les coûts de transactions, nous introduisons un arbitre qui propose des répartitions de surplus et une commune d’accueil. La question principale dans cet article est de déterminer quelle répartition ce dernier doit proposer pour obtenir un accord rapidement. Pour répondre à cette question, nous révisons la structure traditionnelle des jeux coopératifs et testons le pouvoir prédictif de trois concepts de solution généralisés grâce à la réalisation d’expériences en laboratoirecooperative game theory, environmental economics, laboratory experiments, nimby syndrome, noxious facility siting, théorie des jeux coopératifs, économie de l’environnement, économie expérimentale, syndrome nimby, localisation d’équipements générateur de nuisances