The Symmetric Banzhaf Value for Fuzzy Games with a Coalition Structure

In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.

Strategically supported cooperation in dynamic games with coalition structures

The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.

COOPERATIVE GAMES ON CONVEX GEOMETRIES WITH A COALITION STRUCTURE

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~

THE GENERALIZED SYMMETRIC COALITIONAL BANZHAF VALUE FOR MULTICHOICE GAMES WITH A COALITION STRUCTURE

With respect to multichoice games with a coalition structure,a coalitional value named the generalized symmetric coalitional Banzhaf value is defined,which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure.Two axiomatic systems are established:One is enlightened by the characterizations for the symmetric coalitional Banzhaf value,and the other is inspired by the characterizations for the Banzhaf value.

An Axiomatization of Probabilistic Owen Value for Games with Coalition Structure

In the framework of games with coalition structure, we introduce probabilistic Owen value which is an extension of the Owen value and probabilistic Shapley value by considering the situation that not all priori unions are able to cooperate with others. Then we use five axioms of probabilistic efficiency, symmetric within coalitions, symmetric across coalitions applying to unanimity games, strong monotone property and linearity to axiomatize the value.

Using Computational Intelligence Algorithms to Solve the Coalition Structure Generation Problem in Coalitional Skill Games

Coalitional skill games （CSGs） are a simple model of cooperation in an uncertain environment where each agent has a set of skills that are required to accomplish a variety of tasks and each task requires a set of skills to be completed, but each skill is very hard to be quantified and can only be qualitatively expressed. Thus far, many computational questions surrounding CSGs have been studied. However, to the best of our knowledge, the coalition structure generation problem （CSGP）, as a central issue of CSGs, is extremely challenging and has not been well solved. To this end, two different computational intelligence algorithms are herein evaluated： binary particle swarm optimization （BPSO） and binary differential evolution （BDE）. In particular, we develop the two stochastic search algorithms with two-dimensional binary encoding and corresponding heuristic for individual repairs. After that, we discuss some fundamental properties of the proposed heuristic. Finally, we compare the improved BPSO and BDE with the state-of-the-art algorithms for solving CSGP in CSGs. The experimental results show that our algorithms can find the same near optimal solutions with the existing approaches but take extremely short time, especially under the large problem size.