Star-shaped mediation in influence games

We are interested in analyzing the properties of multi-agent systems [13] where a set of agents have to take a decision among two possible alternatives with the help of the social environment or network of the system itself. The ways in which people influence each other through their interactions in a social network and, in particular, the social rules that can be used for the spread of influence have been proposed in an alternative simple game model [11]. However not all individuals play the same role in the process of taking a decision. In this paper we are interested in formalizing and analyzing the simple game model that results in a mediation system. In this scenario we have a social network together with an external participant, the mediator. The mediator can interact, in different degrees, with the agents and thus help to reach a decision.Peer ReviewedPostprint (published version

Measuring satisfaction in societies with opinion leaders and mediators

An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Preprin

Measuring satisfaction and power in influence based decision systems

We introduce collective decision-making models associated with influence spread under the linear threshold model in social networks. We define the oblivious and the non-oblivious influence models. We also introduce the generalized opinion leader–follower model (gOLF) as an extension of the opinion leader–follower model (OLF) proposed by van den Brink et al. (2011). In our model we allow rules for the final decision different from the simple majority used in OLF. We show that gOLF models are non-oblivious influence models on a two-layered bipartite influence digraph. Together with OLF models, the satisfaction and the power measures were introduced and studied. We analyze the computational complexity of those measures for the decision models introduced in the paper. We show that the problem of computing the satisfaction or the power measure is #P-hard in all the introduced models even when the subjacent social network is a bipartite graph. Complementing this result, we provide two subfamilies of decision models in which both measures can be computed in polynomial time. We show that the collective decision functions are monotone and therefore they define an associated simple game. We relate the satisfaction and the power measures with the Rae index and the Banzhaf value of an associated simple game. This will allow the use of known approximation methods for computing the Banzhaf value, or the Rae index to their practical computation.Peer ReviewedPostprint (author's final draft

Structural and computational aspects of simple and influence games

Simple games are a fundamental class of cooperative games. They have a huge relevance in several areas of computer science, social sciences and discrete applied mathematics. The algorithmic and computational complexity aspects of simple games have been gaining notoriety in the recent years. In this thesis we review different computational problems related to properties, parameters, and solution concepts of simple games. We consider different forms of representation of simple games, regular games and weighted games, and we analyze the computational complexity required to transform a game from one representation to another. We also analyze the complexity of several open problems under different forms of representation. In this scenario, we prove that the problem of deciding whether a simple game in minimal winning form is decisive (a problem that is associated to the duality problem of hypergraphs and monotone Boolean functions) can be solved in quasi-polynomial time, and that this problem can be polynomially reduced to the same problem but restricted to regular games in shift-minimal winning form. We also prove that the problem of deciding wheter a regular game is strong in shift-minimal winning form is coNP-complete. Further, for the width, one of the parameters of simple games, we prove that for simple games in minimal winning form it can be computed in polynomial time. Regardless of the form of representation, we also analyze counting and enumeration problems for several subfamilies of these games. We also introduce influence games, which are a new approach to study simple games based on a model of spread of influence in a social network, where influence spreads according to the linear threshold model. We show that influence games capture the whole class of simple games. Moreover, we study for influence games the complexity of the problems related to parameters, properties and solution concepts considered for simple games. We consider extremal cases with respect to demand of influence, and we show that, for these subfamilies, several problems become polynomial. We finish with some applications inspired on influence games. The first set of results concerns to the definition of collective choice models. For mediation systems, several of the problems of properties mentioned above are polynomial-time solvable. For influence systems, we prove that computing the satisfaction (a measure equivalent to the Rae index and similar to the Banzhaf value) is hard unless we consider some restrictions in the model. For OLFM systems, a generalization of OLF systems (van den Brink et al. 2011, 2012) we provide an axiomatization of satisfaction. The second set of results concerns to social network analysis. We define new centrality measures of social networks that we compare on real networks with some classical centrality measures.Los juegos simples son una clase fundamental de juegos cooperativos, que tiene una enorme relevancia en diversas áreas de ciencias de la computación, ciencias sociales y matemáticas discretas aplicadas. En los últimos años, los distintos aspectos algorítmicos y de complejidad computacional de los juegos simples ha ido ganando notoriedad. En esta tesis revisamos los distintos problemas computacionales relacionados con propiedades, parámetros y conceptos de solución de juegos simples. Primero consideramos distintas formas de representación de juegos simples, juegos regulares y juegos de mayoría ponderada, y estudiamos la complejidad computacional requerida para transformar un juego desde una representación a otra. También analizamos la complejidad de varios problemas abiertos bajo diferentes formas de representación. En este sentido, demostramos que el problema de decidir si un juego simple en forma ganadora minimal es decisivo (un problema asociado al problema de dualidad de hipergrafos y funciones booleanas monótonas) puede resolverse en tiempo cuasi-polinomial, y que este problema puede reducirse polinomialmente al mismo problema pero restringido a juegos regulares en forma ganadora shift-minimal. También demostramos que el problema de decidir si un juego regular en forma ganadora shift-minimal es fuerte (strong) es coNP-completo. Adicionalmente, para juegos simples en forma ganadora minimal demostramos que el parámetro de anchura (width) puede computarse en tiempo polinomial. Independientemente de la forma de representación, también estudiamos problemas de enumeración y conteo para varias subfamilias de juegos simples. Luego introducimos los juegos de influencia, un nuevo enfoque para estudiar juegos simples basado en un modelo de dispersión de influencia en redes sociales, donde la influencia se dispersa de acuerdo con el modelo de umbral lineal (linear threshold model). Demostramos que los juegos de influencia abarcan la totalidad de la clase de los juegos simples. Para estos juegos también estudiamos la complejidad de los problemas relacionados con parámetros, propiedades y conceptos de solución considerados para los juegos simples. Además consideramos casos extremos con respecto a la demanda de influencia, y probamos que para ciertas subfamilias, varios de estos problemas se vuelven polinomiales. Finalmente estudiamos algunas aplicaciones inspiradas en los juegos de influencia. El primer conjunto de estos resultados tiene que ver con la definición de modelos de decisión colectiva. Para sistemas de mediación, varios de los problemas de propiedades mencionados anteriormente son polinomialmente resolubles. Para los sistemas de influencia, demostramos que computar la satisfacción (una medida equivalente al índice de Rae y similar al valor de Banzhaf) es difícil a menos que consideremos algunas restricciones en el modelo. Para los sistemas OLFM, una generalización de los sistemas OLF (van den Brink et al. 2011, 2012) proporcionamos una axiomatización para la medida de satisfacción. El segundo conjunto de resultados se refiere al análisis de redes sociales, y en particular con la definición de nuevas medidas de centralidad de redes sociales, que comparamos en redes reales con otras medidas de centralidad clásica

Star-shaped mediation in influence games

We are interested in analyzing the properties of multi-agent systems [13] where a set of agents have to take a decision among two possible alternatives with the help of the social environment or network of the system itself. The ways in which people influence each other through their interactions in a social network and, in particular, the social rules that can be used for the spread of influence have been proposed in an alternative simple game model [11]. However not all individuals play the same role in the process of taking a decision. In this paper we are interested in formalizing and analyzing the simple game model that results in a mediation system. In this scenario we have a social network together with an external participant, the mediator. The mediator can interact, in different degrees, with the agents and thus help to reach a decision.Peer Reviewe