A game theoretic approach to group centrality

This paper is centered in the valuation of the centrality of groups following aproblem-specific approach (Friedkin, 1991). Assuming a TU-game that reflects theinterests which motivate the interactions among individuals in a network, we extend thegame theoretic centrality measure of Gomez et al. (2003) to the case of groups, anddefine the game theoretic group centrality of a group as the variation of its value orpower due to their social relations. We rely on the Shapley group value (Flores et al.,2014) for measuring the value of a group in a game without any restriction, and weintroduce the Myerson group value in order to measure the value when the socialstructure is considered.This research has been supported by I+D+i research project MTM2011-27892 from the Government of Spai

The position value as a centrality measure in social networks

The position value, introduced by Meessen (1988), is a solution concept for cooperative games in which the value assigned to a player depends on the value of the connections or links he has with other players. This concept has been studied by Borm et al. (1992) and characterised by Slikker (2005). In this paper, we analyse the position value from the point of view of the typical properties of a measure of centrality in a social network. We extend the analysis already developed in Gomez et al. (2003) for the Myerson centrality measure, where the symmetric effect on the centralities of the end nodes of an added or removed edge is a fundamental part of its characterisation. However, the Position centrality measure, unlike the Myerson centrality measure, responds in a more versatile way to such addition or elimination. After studying the aforementioned properties, we will focus on the analysis and characterisation of the Position attachment centrality given by the position value when the underlying game is the attachment game. Some comparisons are made with the attachment centrality introduced by Skibski et al. (2019).Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasInstituto de Matemática Interdisciplinar (IMI)FALSEMinisterio de Ciencia e Innovaciónunpu

Some game theoretic marketing attribution models

In this paper, we propose and analyse two game theoretic approaches to design attribution mechanisms for multi-channel marketing campaigns. Both approaches are based on a key performance index function that provides the benefit obtained in each of the observed paths to conversion. The first approach considers the problem as a cooperative transferable utility game, and the proposed attribution mechanisms are based on the Shapley value. The second approach models the problem as a bankruptcy problem and the proposed attribution mechanism is based on the constrained equal-losses rule. We also extend the above approaches to deal with the cases in which the position or the repetition of the channels on the paths to conversion are taken into account

Imputación de costes y beneficios : aportaciones desde la teoría de juegos cooperativos

Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Estadística e Investigación Operativa I, leída el 11-12-1998En esta memoria se estudian algunos aspectos del problema general de cómo repartir el beneficio que se ha generado o el coste en que se ha incurrido cuando un grupo de agentes participa conjuntamente en la producción o el consumo de un bien. Dicho estudio se aborda desde el punto de vista que ofrece la Teoría de Juegos Cooperativos con utilidad transferible. Concretamente, se analizan tres problemas de la economía teórica: el problema de asignación de costes conjuntos de producción de bienes heterogéneos (capítulo 2), el problema de repartir el beneficio que se ha generado con la venta en el mercado de una serie de productos elaborados, mediante un proceso de producción lineal, a partir de recursos controlados por comités de agentes (capítulo 3) y el problema de cómo distribuir el coste de mantenimiento de una red de suministros entre sus usuarios (capítulo 4)Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu

Linear production games with committee control: Limiting behaviour of the core

We study the relation between the core of a given controlled committee LP-game and the set of payoff vectors generated by shadow prices and core allocations of those simple games describing the control over the different resources. The central problem we tackle is the convergence of the core of LP-games with committee control to the set of competitive equilibria, which we define as the set previously described, as the number of players increases uniformly.Generalitat Valenciana (Pla Valencià d'Investigació Científica i Desenvolupament TecnòlogicGobierno de EspañaDepto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu

The equalizer and the lexicographical solutions for cooperative fuzzy games: characterization and properties

In this paper we analyze the lexicographical solution for fuzzy TU games, we study its properties and obtain a characterization. The lexicographical solution was introduced by Sakawa and Nishizaki (Fuzzy Sets and Systems 61 (1994) 265-275) as a solution for crisp TU games, and then extended as a value for fuzzy TU games. We approach the problem by means of the close relationship that exists between the lexicographical solution for crisp TU games and the least square nucleolus, a crisp value defined by Ruiz et al. (Internat. J. Game Theory 25 (1996) 113-134). Previously, and also based on this relationship, we axiomatically characterize the equalizer solution for fuzzy TU games. Both values, the equalizer and the lexicographical solutions, are based on the consideration of a measure of dissatisfaction of players rather than coalitions

Linear production games with fuzzy control

The aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options. In order to model these situations, we consider several kinds of fuzzy controls, which can be modelled as different simple fuzzy games. An LP-game which is an extension of LP-games with committee control introduced in Curiel et al. [on balanced games and games with committee control, OR Spectrum 11 (1989) 83-88] is obtained and its core is studied