Non-cooperative facility location and covering games

Cardinal, Jean; Hoefer, Martin

doi:10.1016/j.tcs.2010.02.005

Cited by 53 publications

(45 citation statements)

References 51 publications

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“…Some of the results were presented in other papers, some of them were presented for related problems and we show how to adapt these results for the facility location. In Section 3, we summarize results for facility location games with no cost sharing rules, mainly from Cardinal and Hoefer [16,18]. In Section 4, results from network design [17] are adapted to fair cost facility location games, and a short compilation of results for the weighted version of the game is presented.…”

Section: Contributions and Text Organizationmentioning

confidence: 99%

“…In [16], Cardinal and Hoefer analyzed a class of covering games which includes FLG and answer a few fundamental questions about it. They proved that there may be instances of FLG with no PNE, also showing that it is NP-Complete to determine whether an instance of FLG has an equilibrium or not.…”

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

“…Theorem 1 (Pure Nash Equilibrium existence for FLG [16]). There are instances of the FLG where there is no PNE.…”

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

“…A game instance for the FLG with no PNE, first described in [16]. Letters next to terminals indicate which player controls the terminal.…”

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

“…How players share the facility opening costs may vary depending on the specific version of the game being analyzed. When there is no rules on how to share opening costs, some important results have been presented by [16]. However, few direct results have been presented for other variants of this game, with most results being adaptations from other problems such as the network design problem [17].…”

Section: Introductionmentioning

confidence: 99%

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Non-Cooperative Facility Location Games: a Survey

Rodrigues¹,

Xavier²

2017

RITA

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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. Uma autoridade central busca determinar uma solução com um custo mínimo, considerando os custos de abertura e conexão, de tal maneira que todos os clientes sejam supridos por uma instalação. Nesta resenha literária, estamos interessados na versão de jogo não cooperativa desse problema, em que, em vez de existir uma autoridade central, cada cliente é um jogador e decide em qual instalação se conectar. Ao escolher a instalação, cada cliente pretende minimizar seus próprios custos, dado pelos custos de conexão e custos de abertura da instalação, que podem ser compartilhados entre os clientes que usam a mesma instalação. Este problema é relevante a várias aplicações práticas, especialmente em cenários distribuídos, onde uma autoridade central é muito dispendiosa ou impossível de existir. Neste artigo, apresentamos uma resenha da literatura existente descrevendo diferentes variantes desse problema e revisando vários resultados sobre eles, além de adaptar os resultados da literatura existente sobre a existência de equilíbrio, Preço da Anarquia e Preço de Estabilidade. Também destacamos alguns problemas em aberto que ainda não foram abordados na literatura. Abstract: 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 connect 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.P...

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Section: Contributions and Text Organizationmentioning

confidence: 99%

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

“…Theorem 1 (Pure Nash Equilibrium existence for FLG [16]). There are instances of the FLG where there is no PNE.…”

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

“…A game instance for the FLG with no PNE, first described in [16]. Letters next to terminals indicate which player controls the terminal.…”

Section: Facility Location Without Cost Sharing Rulesmentioning

confidence: 99%

Section: Introductionmentioning