On fair cost facility location games with non-singleton players

In the fair cost facility location game, players control terminals and must open and connect each terminal to a facility, while paying connection costs and equally sharing the opening costs associated with the facilities it connects to. In most of the literature, it is assumed that each player control a single terminal. We explore a more general version of the game where each player may control multiple terminals. We prove that this game does not always possess pure Nash equilibria, and deciding whether an instance has equilibria is NP-Hard, even in metric instances. Furthermore, we present results regarding the efficiency of equilibria, showing that the price of stability of this game is equal to the price of anarchy, in both uncapacitated and capacitated settings

Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.Comment: 30 pages, 7 figure

Non-Atomic One-Round Walks in Polynomial Congestion Games

Abstract. In this paper we study the approximation ratio of the solutions achieved after an -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions onl

Jogos de localização de instalações não cooperativos e percepção de custos

Orientadores: Eduardo Candido Xavier, Guido SchäferTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Esta tese de doutorado cobre a interseção entre problemas de localização de instalações e teoria dos jogos algorítmica não cooperativa, com ênfase em alterações da percepção de custos de cada jogador e seu efeito na qualidade de equilíbrios. O problema de localização de instalações é um dos problemas fundamentais em otimização combinatória. Em sua versão clássica, existe um conjunto de terminais e um conjunto de instalações, e cada terminal necessita ser conectado a uma instalação, para que esta providencie bens ou serviços. O objetivo é minimizar o total dos custos associados à abertura das instalações e à conexão dos terminais a essas instalações. Na prática, existem diversos cenários onde é inviável ou não é desejável que uma autoridade central única decida como clientes devem escolher as instalações às quais se conectam. Dessa forma, é importante estudar como a independência desses terminais pode afetar a eficiência social e a complexidade computacional para esses cenários. A teoria dos jogos algorítmica pode ser útil para tais cenários, em particular sua parte não cooperativa. A teoria dos jogos algorítmica preenche uma lacuna entre a ciência da computação teórica e a teoria dos jogos, e está interessada em questões como a complexidade computacional de se encontrar equilíbrios, o quanto o bem-estar social pode ser perdido devido ao egoísmo de jogadores e como desenvolver mecanismos para garantir que o melhor interesse dos jogadores se alinhe com o ótimo social. Nesta tese, estudamos jogos de localização de instalações não cooperativos e algumas de suas variantes. Focamos em responder questões relativas à existência de equilíbrios de Nash puros e sobre as principais medidas de perda de eficiência, o preço da anarquia e preço da estabilidade. Apresentamos uma revisão das descobertas mais importantes para as variantes básicas, com novos resultados nos casos onde nenhum era conhecido. Para a versão capacitada desses jogos, mostramos que, enquanto a simultaneidade pode levar a uma perda de eficiência ilimitada, quando se admite a sequencialidade de jogadores, é possível mostrar que a perda de eficiência tem limites. Também investigamos como mudanças na percepção de custo podem afetar a qualidade de equilíbrios de duas maneiras: através de jogadores altruístas e de esquemas de taxação. No primeiro, adaptamos resultados de jogos de compartilhamento justo de custos e apresentamos novos resultados sobre uma versão sem regras de compartilhamento. No último, propomos um modelo de mudança na percepção de custos, onde os jogadores consideram um pedágio adicional em suas conexões ao calcular seus custos. Apresentamos limitantes para o custo total das taxas no problema de pedágios mínimos, onde o objetivo é encontrar o valor mínimo de pedágio necessário para garantir que um determinado perfil de estratégia socialmente ótimo seja escolhido pelos jogadores. Mostramos algoritmos para encontrar pedágios ótimos para tal problema em casos especiais e relacionamos esse problema a um problema de emparelhamento NP-difícilAbstract: This Ph.D. thesis covers the intersection between facility location problems and non-cooperative algorithmic game theory, with emphasis on possible changes in cost perception and its effects in regards to quality of equilibria. The facility location problem is one of the fundamental problems in the combinatorial optimization field of study. In its classic version, there exists a set of terminals and a set of facilities, and each terminal must be connected to a facility, in order for goods or services to be provided. The objective is to minimize the total costs associated with opening the facilities and connecting all the terminals to these facilities. In practice, there are multiple scenarios where it is either infeasible or not desirable for a single central authority to decide which facilities terminals connect to. Thus, it is important to study how the independence of these terminals may affect social efficiency and computational complexity in these scenarios. For this analysis algorithmic game theory can be of use, in particular its non-cooperative part. Algorithmic game theory bridges a gap between theoretical computer science and game theory, and is interested in questions such as how hard it is computationally to find equilibria, how much social welfare can be lost due to player selfishness and how to develop mechanisms to ensure that players' best interest align with the social optimum. In this thesis we study non-cooperative facility location games and several of its variants. We focus on answering the questions concerning the existence of pure Nash equilibria and the main measures of efficiency loss, the price of anarchy and the price of stability. We present a review of the most important findings for the basic variants and show new results where none were known. For the capacitated version of these games, we show that while simultaneity may lead to unbounded loss of efficiency, when sequentiality is allowed, it is possible to bound the efficiency loss. We also investigate how changes in players' perception of cost can affect the efficiency loss of these games in two ways: through altruistic players and through tolling schemes. In the former we adapt results from fair cost sharing games and present new results concerning a version with no cost sharing rules. In the latter, we propose a model for change in cost perception where players consider an additional toll in their connections when calculating their best responses. We present bounds for total toll cost in the minimum toll problem, where the objective is to find the minimum amount of tolls needed to ensure that a certain socially optimal strategy profile will be chosen by players. We show algorithms for finding optimal tolls for the minimum toll problem in special cases and provide some insight into this problem by connecting it to a matching problem which we prove is NP-hardDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação147141/2016-8CAPESCNP

Stackelberg strategies for network design games

International audienceWe consider the network-design game introduced by Anshelevich et al. in which n source–destination pairs must be connected by n respective players equally sharing the cost of the used links. It is well known that the price of anarchy for this class of games may be as large as n. One approach for reducing this bound is that of resorting to the Stackelberg model, in which for a subset of at most ⌊αn⌋ coordinated players, with 0⩽α⩽1, communication paths inducing better equilibria are fixed. In this paper we show the effectiveness of Stackelberg strategies by providing optimal and nearly optimal bounds on the performance achievable by such Stackelberg strategies. In particular, in contrast to previous works, we are also able to provide Stackelberg strategies computable in polynomial time and lowering the price of anarchy from n to . Most of the results are extended to the case in which each player aims at connecting k>2 nodes of the network