Estudio y caracterización de soluciones para juegos cooperativos y bicooperativos

• Autores: Margarita Doménech Blázquez
• Directores de la Tesis: María Albina Puente del Campo (dir. tes.) , José Miguel Jiménez Pradales (codir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2020
• Idioma: español
• Texto completo no disponible (Saber más ...)
• Resumen

  • The first part of this thesis focuses on cooperative games and specifically on the study of semivalues and probabilistic values. 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 in lower cardinalities, we will study the recovery of its weighting coefficients from the last weighting coefficients of its induced semivalues. Moreover, we will provide the conditions of a sequence of numbers so that they are the family of the last coefficients of any induced semivalues. As a consequence of this fact, we will 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. We will see that multinomial probabilistic values constitute a consistent alternative to classical values such as those of Shapley and Banzhaf. These values were introduced in Reliability Systems called multibinary probabilistic values. Here we will study them for cooperative games from different points of view and, especially, as a powerful generalization of binomial semivalues. We will give necessary and / or sufficient conditions for the coefficients of the probabilistic values in general and for the multinomial values in particular, so that certain standard properties in the context of Game Theory are satisfied. Finally, we will define the p-potential function for multinomial probabilistic values with a positive tendency profile.

    The second part of the work focuses on bicooperative games. Here we introduce the bisemivalues for these games, giving a characterization of them by means of weighting coefficients, in a similar way as it was given for semivalues in the context of cooperative games. Following the same line of study on the cooperative case, we introduce a subfamily of these values, called (p,q) - bisemivalues and, as a particular case of it, the binomial bisemivalues, which extends the concept of binomial values to bicooperative games. We will also present several properties for values in bicooperatives games with respect to null and nonnull players, balanced contributions, dominance, monotony and sensitivity and block formation, that parallels a series of standard properties considered for values on cooperative games in the literature on value theory. We will also study the behavior of the bisemivalues with respect to them, the characterization of some subfamily of bisemivalues arises in a natural way as a convenient condition to guarantee the validity of some of them. We will provide axiomatic characterizations of the Banzhaf and the Shapley bisemivalues.We will give computational procedures based on the multilinear extension of the game to calculate bisemivalues in general and the (p,q) - bisemivalues in particular. Finally, we also provide a computational procedure to calculate the allocations given by the Shapley bisemivalue in terms of the generalized multilinear extension of the game..