Estrategias de seguridad Pareto óptimas en modelos de interacción entre empresas

La Teoría de Juegos estudia situaciones conflictivas, alguna de ellas clásicas como el dilema del prisionero, donde se ponen de manifiesto los problemas que surgen al considerar los puntos de equilibrio como concepto de solución para juegos de suma no nula. Estas dificultades pueden provenir tanto de la existencia de múltiples puntos de equilibrio como de la no eficiencia de los pagos que proporcionan. En este trabajo aplicamos un análisis alternativo para juegos simétricos 2x2 de suma no nula, cuya estructura estratégica se adapta a gran variedad de problemas económicos competitivos. Analizándolos como juegos matriciales bicriterio, proporcionamos soluciones que son independientes de la noción de equilibrio, de forma que un jugador sólo considera a su adversario para establecer los niveles de seguridad.Game Theory studies conflicts situations, some of them classic as the prisoner’s dilemma, (between people) where problems for the applicability of the concept of equilibrium, as an unquestionable solution concept, for non-zero sum games, are shown. These difficulties might come from the multiplicity of Nash equilibrium, as well as from the inefficiency of the associated payoffs. In this paper we consider a new way to analyze 2x2 bimatrix non-zero sum games, which include a wide variety of important social and economic situations. This new approach consists of considering the games as vicriteria matrix games that allow to provide security strategies based on Parteo optimality. This solution concept is independent of the notion of eequilibrium, so that the opponent is only taken into account to establish the security levels for one’s own payoff

Game Theory

The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner

Estructura Combinatoria de Politopos asociados a Medidas Difusas

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 23-11-2020This PhD thesis is devoted to the study of geometric and combinatorial aspects of polytopes associated to fuzzy measures. Fuzzy measures are an essential tool, since they generalize the concept of probability. This greater generality allows applications to be developed in various elds, from the Decision Theory to the Game Theory. The set formed by all fuzzy measures on a referential set is a polytope. In the same way, many of the most relevant subfamilies of fuzzy measures are also polytopes. Studying the combinatorial structure of these polytopes arises as a natural problem that allows us to better understand the properties of the associated fuzzy measures. Knowing the combinatorial structure of these polytopes helps us to develop algorithms to generate points uniformly at random inside these polytopes. Generating points uniformly inside a polytope is a complex problem from both a theoretical and a computational point of view. Having algorithms that allow us to sample uniformly in polytopes associated to fuzzy measures allows us to solve many problems, among them the identi cation problem, i.e. estimate the fuzzy measure that underlies an observed data set...La presente tesis doctoral esta dedicada al estudio de distintas propiedades geometricas y combinatorias de politopos de medidas difusas. Las medidas difusas son una herramienta esencial puesto que generalizan el concepto de probabilidad. Esta mayor generalidad permite desarrollar aplicaciones en diversos campos, desde la Teoría de la Decision a laTeoría de Juegos. El conjunto formado por todas las medidas difusas sobre un referencial tiene estructura de politopo. De la misma forma, la mayora de las subfamilias mas relevantes de medidas difusas son tambien politopos. Estudiar la estructura combinatoria de estos politopos surge como un problema natural que nos permite comprender mejor las propiedades delas medidas difusas asociadas. Conocer la estructura combinatoria de estos politopos tambien nos ayuda a desarrollar algoritmos para generar aleatoria y uniformemente puntos dentro de estos politopos. Generar puntos de forma uniforme dentro de un politopo es un problema complejo desde el punto de vista tanto teorico como computacional. Disponer de algoritmos que nos permitan generar uniformemente en politopos asociados a medidas difusas nos permite resolver muchos problemas, entre ellos el problema de identificacion que trata de estimarla medida difusa que subyace a un conjunto de datos observado...Fac. de Ciencias MatemáticasTRUEunpu

A methodology for quantitative and cooperative decision making of air mobility operational solutions

Many complex and interdependent systems engineering challenges involve more than one stakeholder or decision maker. These challenges, such as the definition and acquisition of future air mobility systems, are often found in situations where resources are finite, objectives are conflicting, constraints are restricting, and uncertainty in future outcomes prevail. Air mobility operational models which simulate fleet wide behavior effects over time, in various mission scenarios, and potentially over the entire design life-cycle, are always multi-dimensional, cover a large decision space, and require significant time to generate sufficient solutions to adequately describe the design space. This challenge is coupled with the fact that, in these highly integrated solutions or acquisitions, multiple stakeholders or decision makers are required to cooperate and reach agreement in selecting or defining the requirements for the design or solution and in its costly and lengthy implementation. However, since values, attitudes, and experiences are different for each decision maker, reaching consensus across the multiple criteria with different preferences and objectives is often a slow and highly convoluted process. In response to these common deficiencies and to provide quantitative analyses, this research investigates and proposes solutions to two challenges: 1) increase the speed at which operational solutions and associated requirements are generated and explored, and 2) systematize the group decision-making process, to both accelerate and improve decision making in these large operational problems requiring cooperation. The development of the Air Mobility Operations Design (AirMOD) model is proposed to address the first challenge by implementing and leveraging surrogate models of airlift capability across a wide scenario space. In addressing the second major challenge, the proposed Multi-Agent Consensus Reaching on the Objective Space (MACRO) methodology introduces a process to reduce the feasible decision space, by identifying regions of high probability of consensus reaching, using preference distributions, power relationships, and game-theoretic techniques. In a case study, the MACRO methodology is demonstrated on a large air mobility solution space generated by AirMOD to illustrate plausibility of the overall approach. AirMOD and MACRO offer considerable advantages over current methods to better define the operational design space and improve group decision-making processes requiring cooperation, respectively.Ph.D