Associated consistency and values for TU games

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache's axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide

Associated consistency and values for TU games

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide. \u

Matrix approach to consistency of the additive efficient normalization of semivalues

In fact the Shapley value is the unique efficient semivalue. This motivated Ruiz et al. to do additive efficient normalization for semivalues. In this paper, by matrix approach we derive the relationship between the additive efficient normalization of semivalues and the Shapley value. Based on the relationship, we axiomatize the additive efficient normalization of semivalues as the unique solution verifying covariance, symmetry, and reduced game property with respect to the $p-$reduced game

Estado del arte para un sistema de información para la valoración estratégica y financiera de las empresas que desean cooperar en un clúster, basada en el valor de shapley

Bahinipati et al. (2009) [16] proponen un plan de reparto de ingresos y participantes de coaliciones en el mercado eléctrico de la Industria de semiconductores. Como resultado de la investigación se concluyó que el beneficio total derivado del mecanismo desarrollado, incrementaba con el número de eslabones de la Cadena de Suministro. Ahmadi y Hoseinpour (2011) [17] estudian la coordinación de decisiones de publicidad en conjunto de una cadena de suministro conformada por Fabricante y Minorista, utilizando distintos modelos propios de la Teoría de juegos y analizando las posibles acciones de cada jugador dado ciertos escenarios

Axioms of invariance for TU-games

We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TU-games. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used

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