Matrix analysis for associated consistency in cooperative game theory

Hamiache's recent axiomatization of the well-known Shapley value for TU games states that the Shapley value is the unique solution verifying the following three axioms: the inessential game property, continuity and associated consistency. Driessen extended Hamiache's axiomatization to the enlarged class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. Particularly, both the Shapley value and the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix $M^{Sh}$ and the associated transformation matrix $M_\lambda,$ respectively. We develop a matrix approach for Hamiache's axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality $M^{Sh}=M^{Sh}·M_\lambda.$ The diagonalization procedure of $M_\lambda$ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen's axiomatization of a certain class of linear values. Matrix analysis is adopted throughout both the mathematical developments and the proofs. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory

A solution set for fine games

Bumb and Hoede have shown that a cooperative game can be split into two games, {\it the reward game} and {\it the fine game}, by considering the sign of quantities $c_S^v$ in the c-diagram of the game. One can then define a solution $x$ for the original game as $x=x_{r}-x_{f}$, where $x_{r}$ is a solution for the reward game and $x_{f}$ is a solution for the fine game. Due to the distinction of cooperation rewards and fines, for allocating the fines one may use another solution concept than for the rewards

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

Effects of Ru Substitution on Dimensionality and Electron Correlations in Ba(Fe_{1-x}Ru_x)_2As_2

We report a systematic angle-resolved photoemission spectroscopy study on Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ for a wide range of Ru concentrations (0.15 $\leq$ \emph{x} $\leq$ 0.74). We observed a crossover from two-dimension to three-dimension for some of the hole-like Fermi surfaces with Ru substitution and a large reduction in the mass renormalization close to optimal doping. These results suggest that isovalent Ru substitution has remarkable effects on the low-energy electron excitations, which are important for the evolution of superconductivity and antiferromagnetism in this system.Comment: 4 pages, 4 figure

A solution defined by fine vectors

Bumb and Hoede have shown that a cooperative game can be split into two games, the reward game and the fine game, by considering the sign of quantities $c_v^S$ in the c-diagram of the game. One can then define a solution $x$ for the original game as $x = x_r - x_f$ , where $x_r$ is a solution for the reward game and $x_f$ is a solution for the fine game. Due to the distinction of cooperation rewards and fines, for allocating the fines one may use another solution concept than for the rewards. In this paper, a fine vector is introduced and a solution is defined by fine vectors. The structure and properties of this solution are studied. And the solution is characterized as the unique solution having efficiency and f-potential property (resp. f-balanced contributions property)

Unambiguous Acquisition and Tracking Technique for General BOC Signals

This article presents a new unambiguous acquisition and tracking technique for general Binary Offset Carrier (BOC) ranging signals, which will be used in modern GPS, European Galileo system and Chinese BeiDou system. The test criterion employed in this technique is based on a synthesized correlation function which completely removes positive side peaks while keeping the sharp main peak. Simulation results indicate that the proposed technique completely removes the ambiguity threat in the acquisition process while maintaining relatively higher acquisition performance for low order BOC signals. The potential false lock points in the tracking phase for any order BOC signals are avoided by using the proposed method. Impacts of thermal noise and multipath on the proposed technique are investigated; the simulation results show that the new method allows the removal of false lock points with slightly degraded tracking performance. In addition, this method is convenient to implement via logic circuits