Semivalues: weighting coefficients and allocations on unanimity games

This is a post-peer-review, pre-copyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590-017-1224-8.Each semivalue, as a solution concept defined on cooperative games with a finite set of players, is univocally determined by weighting coefficients that apply to players’ marginal contributions. Taking into account that a semivalue induces semivalues on lower cardinalities, we prove that its weighting coefficients can be reconstructed from the last weighting coefficients of its induced semivalues. Moreover, we provide the conditions of a sequence of numbers in order to be the family of the last coefficients of any induced semivalues. As a consequence of this fact, we give two characterizations of each semivalue defined on cooperative games with a finite set of players: one, among all semivalues; another, among all solution concepts on cooperative games.Peer ReviewedPostprint (author's final draft

Some properties for probabilistic and multinomial (probabilistic) values on cooperative games

This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 18-02-2016, available online: http://www.tandfonline.com/10.1080/02331934.2016.1147035.We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.Peer ReviewedPostprint (author's final draft

Multinomial probabilistic values

Multinomial probabilistic values were introduced by one of us in reliability. Here we define them for all cooperative games and illustrate their behavior in practice by means of an application to the analysis of a political problem.Peer ReviewedPostprint (author’s final draft

Bayesian Regression Markets

Machine learning tasks are vulnerable to the quality of data used as input. Yet, it is often challenging for firms to obtain adequate datasets, with them being naturally distributed amongst owners, that in practice, may be competitors in a downstream market and reluctant to share information. Focusing on supervised learning for regression tasks, we develop a \textit{regression market} to provide a monetary incentive for data sharing. Our proposed mechanism adopts a Bayesian framework, allowing us to consider a more general class of regression tasks. We present a thorough exploration of the market properties, and show that similar proposals in current literature expose the market agents to sizeable financial risks, which can be mitigated in our probabilistic setting.Comment: 46 pages, 11 figures, 2 table

Coalitional control in the framework of cooperative game theory

[EN] Coalitional control is a fairly new branch of distributed control where the agents merge dynamically into coalitions according to the enabled/disabled communication links at each time instant. Therefore, with these schemes there is a reduction of the communication burden without compromising the system performance. In this tutorial, the main features of these schemes will be introduced in the framework of cooperative game theory, being the game related to the cost function that is optimized by the control approach, and with the players corresponding to either the communication links or the agents involved. In this context, several cooperative game theory tools will be considered in order to: rank the players, impose constraints on them, provide more effcient ways of calculation, perform system partitioning, etc., hence analyzing the main features related to each tool.[ES] El control coalicional es una rama incipiente del control distribuido donde los distintos agentes se agrupan de forma dinámica en coaliciones en función de los enlaces de comunicación activos/inactivos en cada instante de tiempo. Gracias a ello, se reduce la carga de comunicación sin comprometer las prestaciones del sistema. En este tutorial, se analizan las principales características de estos esquemas dentro del marco de la teoría de juegos cooperativos, estando el juego definido por la función de coste a optimizar en el esquema de control, y correspondiendo los jugadores bien a los enlaces de comunicación o bien a los propios agentes. En este contexto, se estudiarán diversas herramientas de teoría de juegos cooperativos, con objeto de clasificar jugadores, imponer restricciones en los mismos, proponer vías de cálculo más eficientes, realizar particionado de sistemas, etc., examinando las características más relevantes presentadas por cada herramienta.Este estudio ha sido parcialmente financiado por los proyectos de investigación OCONTSOLAR, (H2020 ADG-ERC, ID 789051), C3PO (MINECO, DPI2017-86918-R), y GESVIP (Junta de Andalucía, US-1265917). Asimismo, se agradece a Jose María Maestre, Encarnación Algaba y Eduardo F. Camacho las innumerables discusiones mantenidas a lo largo de los anos de doctorado que me ayudaron a dominar los conceptos presentados en este tutorial. Es también de destacar los comentarios del Editor y los revisores anónimos que han contribuido a la mejora sustancial del manuscrito. Finalmente, se dedica este artículo a Lloyd S. 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