The team of this project, consisting of nine mathematicians, aims to develop their research in two broad areas: voting games and games of cooperation, in their mathematical, computational and social aspects, areas in which the group has accumulated extensive experience over the past two decades. Some of the proposed objectives can be considered an extension of the work developed by the group in the existing project with MTM- 34426 code, since the progress achieved till now has opened new and challenging prospects. But, furthermore, other more innovative goals are also pursued in the project, such as computational complexity analysis or studies which venture into social choice aspects, as influence nets or collective decision models. The research history of the team in these fields is still reduced but our knowledge and analysis capacity, together with the accumulated experience in game theory, assure our skills to develop the proposed goals with great competence. The project is structured around the following specific activities: 1. Voting games with alternatives: axiomatic characterizations, mathematical structure and applications. 2. Simple games with probability distributions associated to coalitions: theory and practice. 3. Study of bibliometric measures and evaluations of committees in sports or social contexts. 4. Study of properties of multinomial probability values; semivalues characterization through games of unanimity and introduction of probabilistic coalitional values. 5. Study of semivalues for bicooperative games. 6. Study of parameters, properties and solutions concepts in influence games. 7. Study of models of collective decision and measures of centrality. The studies to be developed will either give an answer or provide suggestions for solving problems in social contexts: analysis of current voting systems (EU and other international organizations or national parliaments); analysis of evaluation committees in economical, political, social, legal, academic or sport contexts; analysis of social networks and of the spread of influence on the agents involved in decision-making models. We expect to get new theoretical and applied results to be published in pretigious journals.
Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016
Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia
Subprograma Estatal de Generación de Conocimiento
Excelencia: Proyectos I+D
Gobierno De España. Ministerio De Economía Y Competitividad, Mineco