99,824 research outputs found
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 and the associated transformation matrix 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 The diagonalization procedure of 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 in the c-diagram of the game. One can then define a solution for the original game as , where is a solution for the reward game and 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 reduced game
Achieving Effective Innovation Based On TRIZ Technological Evolution
Organised by: Cranfield UniversityThis paper outlines the conception of effective innovation and discusses the method to achieve it. Effective
Innovation is constrained on the path of technological evolution so that the corresponding path must be
detected before conceptual design of the product. The process of products technological evolution is a
technical developing process that the products approach to Ideal Final Result (IFR). During the process, the
sustaining innovation and disruptive innovation carry on alternately. By researching and forecasting potential
techniques using TRIZ technological evolution theory, the effective innovation can be achieved finally.Mori Seiki – The Machine Tool Compan
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 in the c-diagram of the game. One can then define a solution for the original game as , where is a solution for the reward game and 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)
Multivalley engineering in semiconductor microcavities
We consider exciton-photon coupling in semiconductor microcavities in which
separate periodic potentials have been embedded for excitons and photons. We
show theoretically that this system supports degenerate ground-states appearing
at non-zero in-plane momenta, corresponding to multiple valleys in reciprocal
space, which are further separated in polarization corresponding to a
polarization-valley coupling in the system. Aside forming a basis for
valleytronics, the multivalley dispersion is predicted to allow for spontaneous
momentum symmetry breaking and two-mode squeezing under non-resonant and
resonant excitation, respectively.Comment: Manuscript: 7 pages, 7 figures, published in Scientific Reports 7,
45243 (2017
Ground-state phases of rung-alternated spin-1/2 Heisenberg ladder
The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg
ladder with rung alternation is studied by combining analytical approaches with
numerical simulations. For the case of ferromagnetic leg exchanges a unique
ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic
leg exchanges several different ground states are stabilized depending on the
ratio between exchanges along legs and rungs. For the more general case of a
honeycomb-ladder model for the case of ferromagnetic leg exchanges besides
usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic
Luttinger liquid phase with both linear and quadratic low energy dispersions
and ground state magnetization continuously changing with system parameters.
For the case of antiferromagnetic exchanges along legs, different dimerized
states including states with additional topological order are suggested to be
realized
The Child is Father of the Man: Foresee the Success at the Early Stage
Understanding the dynamic mechanisms that drive the high-impact scientific
work (e.g., research papers, patents) is a long-debated research topic and has
many important implications, ranging from personal career development and
recruitment search, to the jurisdiction of research resources. Recent advances
in characterizing and modeling scientific success have made it possible to
forecast the long-term impact of scientific work, where data mining techniques,
supervised learning in particular, play an essential role. Despite much
progress, several key algorithmic challenges in relation to predicting
long-term scientific impact have largely remained open. In this paper, we
propose a joint predictive model to forecast the long-term scientific impact at
the early stage, which simultaneously addresses a number of these open
challenges, including the scholarly feature design, the non-linearity, the
domain-heterogeneity and dynamics. In particular, we formulate it as a
regularized optimization problem and propose effective and scalable algorithms
to solve it. We perform extensive empirical evaluations on large, real
scholarly data sets to validate the effectiveness and the efficiency of our
method.Comment: Correct some typos in our KDD pape
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