Algorithm Instance Games

This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of the algorithm's description influence agents' strategic behavior? We analyze two versions of an AIG based on the set-cover optimization problem. In these games, joint strategies correspond to instances of the set-cover problem, with each subset (of a given universe of elements) representing the strategy of a single agent. Outcomes are covers computed from the joint strategies by a set-cover algorithm. In one variant of this game, outcomes are computed by a deterministic greedy algorithm, and the other variant utilizes a non-deterministic form of the greedy algorithm. We characterize Nash equilibrium strategies for both versions of the game, finding that agents' strategies can vary considerably between the two settings. In particular, we find that the version of the game based on the deterministic algorithm only admits Nash equilibrium in which agents choose strategies (i.e., subsets) containing at most one element, with no two agents picking the same element. On the other hand, in the version of the game based on the non-deterministic algorithm, Nash equilibrium strategies can include agents with zero, one, or every element, and the same element can appear in the strategies of multiple agents.Comment: 14 page

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

On the effectiveness of connection tolls in fair cost facility location games

We investigate the effectiveness of tolls to reduce the inefficiency of Nash equilibria in the classical fair cost facility location game. In this game, every terminal corresponds to a selfish player who wants to connect to some facility at minimum cost. The cost of a player is determined by the connection cost to the chosen facility plus an equal share of its opening cost. We are interested in the problem of imposing tolls on the connections to induce a socially optimal Nash equilibrium such that the total amount of tolls is minimized. It turns out that this problem is challenging to solve even for simple special cases. We provide polynomial-time algorithms for (i) instances with two facilities, and (ii) instances with a constant number of facilities arranged as a star. Our algorithm for (ii) exploits a relation between our tolling problem and a novel bipartite matching problem without crossings, which we prove to be NP-hard

Estado del arte para un sistema de información para la valoración estratégica y financiera de las empresas que desean cooperar en un clúster, basada en el valor de shapley

Bahinipati et al. (2009) [16] proponen un plan de reparto de ingresos y participantes de coaliciones en el mercado eléctrico de la Industria de semiconductores. Como resultado de la investigación se concluyó que el beneficio total derivado del mecanismo desarrollado, incrementaba con el número de eslabones de la Cadena de Suministro. Ahmadi y Hoseinpour (2011) [17] estudian la coordinación de decisiones de publicidad en conjunto de una cadena de suministro conformada por Fabricante y Minorista, utilizando distintos modelos propios de la Teoría de juegos y analizando las posibles acciones de cada jugador dado ciertos escenarios

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

Bounds on the Cost of Stabilizing a Cooperative Game

This is the author accepted manuscript. The final version is available from the AI Access Foundation via the DOI in this record.A key issue in cooperative game theory is coalitional stability, usually captured by the notion of the core—the set of outcomes that are resistant to group deviations. However, some coalitional games have empty cores, and any outcome in such a game is unstable. We investigate the possibility of stabilizing a coalitional game by using subsidies. We consider scenarios where an external party that is interested in having the players work together offers a supplemental payment to the grand coalition, or, more generally, a particular coalition structure. This payment is conditional on players not deviating from this coalition structure, and may be divided among the players in any way they wish. We define the cost of stability as the minimum external payment that stabilizes the game. We provide tight bounds on the cost of stability, both for games where the coalitional values are nonnegative (profit-sharing games) and for games where the coalitional values are nonpositive (cost-sharing games), under natural assumptions on the characteristic function, such as superadditivity, anonymity, or both. We also investigate the relationship between the cost of stability and several variants of the least core. Finally, we study the computational complexity of problems related to the cost of stability, with a focus on weighted voting games.DFGEuropean Science FoundationNRF (Singapore)European Research CouncilHorizon 2020 European Research Infrastructure projectIsrael Science FoundationIsrael Ministry of Science and TechnologyGoogle Inter-University Center for Electronic Markets and AuctionsEuropean Social Fund (European Commission)Calabria Regio

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