a simplified expression of the shapley function for fuzzy game abstract in this paper a simplified expression of the shapley function for games with fuzzy coalition is proposed which can be regarded as the generalization of shapley functions defined in some particular games with fuzzy coalition the simplified expression of the shapley function is compared with two definitions established by butnariu tsurumi et al a conclusion is drawn that the simplified expression of the shapley function is equivalent to butnariu s definition when characteristic function is a game with proportional values and is equivalent to tsurumi s definition when characteristic function is a game with choquet integral forms furthermore from an angle of interaction between two participation levels the properties of the two games defined by butnariu and tsurumi are respectively studied

a banzhaf function for a fuzzy game in this paper another important solution for fuzzy games called the banzhaf function is investigated first a sim plified expression for the banzhaf function for games with fuzzy coalition is proposed the relationship between this simplified ex pression and two kinds of particular banzhaf functions are dis cussed in detail furthermore in the framework of games with fuzzy coalitions we give a definition of the potential function of fuzzy games and prove that the marginal values of the potential function are the components of the banzhaf function further more a new axiomatic characterization of the banzhaf function for games with fuzzy coalitions is provided

on cores and stable sets for fuzzy games in this paper cores and stable sets for games with fuzzy coalitions are introduced and their relations studied for convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set also relations between cores and stable sets of fuzzy clan games are discussed

shapley mappings and the cumulative value for n person games with fuzzy coalitions abstract in this paper we prove existence and uniqueness of the so called shapley mapping which is a solution concept for a class of n person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions the shapley mapping when it exists associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency the symmetry and the null player conditions it determines a cumulative value that is the sum of all coalitional allocations for whose computation we provide an explicit formula

fuzzy approaches to the game of chicken game theory deals with decision making processes involving two or more parties also known as players with partly or completely conflicting interests decision makers in a conflict must often make their decisions under risk and under unclear or fuzzy information in this paper two distinct fuzzy approaches are employed to investigate an extensively studied 2 spl times 2 game model the game of chicken the first approach uses a fuzzy multicriteria decision analysis method to obtain optimal strategies for the players it incorporates subjective factors into the decision makers objectives and aggregates objectives using a weight vector the second approach applies the theory of fuzzy moves tfm to the game of chicken the theory of moves tom is designed to bring a dynamic dimension to the classical theory of games by allowing decision makers to look ahead for one or several steps so that they can make a better decision tom is the crisp counterpart of tfm the approach we implement here to deal with games that include fuzzy and uncertain information the application of fuzzy approaches to the game of chicken demonstrates their effectiveness in manipulating subjective uncertain and fuzzy information and provides valuable insights into the strategic aspects of chicken

shapley shubik and banzhaf indices revisited we provide a new axiomatization of the shapley shubik and the banzhaf power indices in the domain of simple superadditive games by means of transparent axioms only anonymity is shared with the former characterizations in the literature the rest of the axioms are substituted by more transparent ones in terms of power in collective decision making procedures in particular a clear restatement and a weaker alternative for the transfer axiom are proposed only one axiom differentiates the characterization of either index and these differentiating axioms provide a new point of comparison in a first step both indices are characterized up to a zero and a unit of scale then both indices are singled out by simple normalizing axioms

potential value and consistency let p be a real valued function defined on the space of cooperative games with transferable utility satisfying the following condition in every game the marginal contributions of all players are efficient it is proved that there exists just one such function p called the potential and moreover that the resulting payoff vector coincides with the shapley value

new mathematical properties of the banzhaf value abstract a new axiomatic characterization of the banzhaf value for a cooperative n person game with transferable utilities is given by using a new potential function in the space of all games with a fixed set of players a potential basis has been found which allows an explicit representation of all games with an apriori given banzhaf value

on the asymptotic s n structure of invariant differential operators on symplectic manifolds abstract we consider the space of polydifferential operators on n functions on symplectic manifolds invariant under symplectic automorphisms whose study was initiated by mathieu in 1995 permutations of inputs yield an action of s n which extends to an action of s n 1 we study this structure viewing n as a parameter in the sense of deligne s category for manifolds of dimension 2d we show that the isotypic part of this space of 2 d 1 th tensor powers of the reflection representation h c n of s n 1 is spanned by poisson polynomials we also prove a partial converse and compute explicitly the isotypic part of 4 th tensor powers of the reflection representation we give generating functions for the isotypic parts corresponding to young diagrams which only differ in the length of the top row and prove that they are rational fractions whose denominators are related to hook lengths of the diagrams obtained by removing the top row this also gives such a formula for the same isotypic parts of induced representations from z n 1 to s n 1 where n is viewed as a parameter we show that the space of invariant operators of order 2m has polynomial dimension in n of degree equal to 2m while the part not coming from poisson polynomials has polynomial dimension of degree 2 m 3 we use this to compute asymptotics of the dimension of invariant operators we also give new bounds on the order of invariant operators for a fixed n we apply this to the poisson and hochschild homology associated to the singularity c 2 d n s n 1 namely the canonical surjection from hp 0 o c 2 d n s n 1 o c 2 d n to gr hh 0 weyl c 2 d n s n 1 weyl c 2 d n the brylinski spectral sequence in degree zero restricts to an isomorphism in the aforementioned isotypic part h 2 d 1 and also in h 4 we prove a partial converse finally the kernel of the entire surjection has dimension on the order of 1 n 3 times the dimension of the homology group

an extension of cooperative fuzzy games in this paper a generalized form of fuzzy game is proposed that can be seen as an extension of the cooperative fuzzy game players in the proposed fuzzy game do not need to know precise information about the payoff value or to form a crisp coalition based on the hukuhara difference a game with a fuzzy characteristic function is studied and the explicit form of a shapley function is shown furthermore we introduce and investigate a new class of fuzzy game with fuzzy coalitions and a fuzzy characteristic function based on the hukuhara difference and the choquet integral we give the explicit form of the shapley value for the new class of fuzzy game it has been seen that most of the properties of a crisp game hold well in the proposed fuzzy game a practical application of the proposed model in joint production problem is also provided

homologie des invariants d une algebre de weyl sous l action d un groupe fini resume soit g un sous groupe fini de sp 2 n c operant par automorphismes dans l algebre de weyl a n c nous calculons les groupes d homologie et de cohomologie de hochschild de l algebre d invariants a n c g let g be a finite subgroup of sp 2 n c acting by automorphisms in the weyl algebra a n c we compute the hochschild homology and cohomology groups of the invariant algebra a n c g

a shapley function on a class of cooperative fuzzy games abstract in this paper we make a study of the shapley values for cooperative fuzzy games games with fuzzy coalitions which admit the representation of rates of players participation to each coalition a shapley function has been introduced by another author as a function which derives the shapley value from a given pair of a fuzzy game and a fuzzy coalition however the previously proposed axioms of the shapley function can be considered unnatural furthermore the explicit form of the function has been given only on an unnatural class of fuzzy games we introduce and investigate a more natural class of fuzzy games axioms of the shapley function are renewed and an explicit form of the shapley function on the natural class is given we make sure that the obtained shapley value for a fuzzy game in the natural class has several rational properties finally an illustrative example is given

fuzzy nash equilibriums in crisp and fuzzy games in this paper we introduce fuzzy nash equilibrium to determine a graded representation of nash equilibriums in crisp and fuzzy games this interpretation shows the distribution of equilibriums in the matrix form of a game and handles uncertainties in payoffs in addition a new method to rank fuzzy values with the user s viewpoint is investigated by this means the definition of satisfaction function which provides the result of comparison in the form of real value is developed when users have preferences regarding the payoffs

a coalitional extension of generalized fuzzy games abstract in this paper we give a coalitional extension of generalized fuzzy games and introduce the notion of coalitional fuzzy equilibria we first prove the existence of coalitional fuzzy equilibria in our model as an application we further show the existence theorem of strong fuzzy equilibria for fuzzy games

non linear normal modes and invariant manifolds small amplitude motions of dynamic systems structural fluid control etc about an equilibrium state are modeled by linear differential equations which have constant coefficients these are typically obtained by a taylor series expansion of the forces about the equilibrium point under quite general circumstances these equations admit a set of special solutions called normal mode motions in which each system component moves with the same frequency and with a fixed ratio amongst the displacements of the components for a conservative system for a non conservative system all displacements and velocities are linearly related to a single displacement velocity pair

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

linear quadratic uncertain differential game with application to resource extraction problem uncertain differential game investigates interactive decision making of players over time and the system dynamics is described by an uncertain differential equation this paper goes further to study the two player zero sum uncertain differential game in order to guarantee the saddle point nash equilibrium a max min theorem is provided furthermore when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic the existence of saddle point nash equilibrium is obtained via the solvability of a corresponding riccati equation finally a resource extraction problem is analyzed by using the theory proposed in this paper

a fuzzy approach to strategic games a game is a decision making situation with many players each having objectives that conflict with each other the players involved in the game usually make their decisions under conditions of risk or uncertainty in the paper a fuzzy approach is proposed to solve the strategic game problem in which the pure strategy set for each player is already defined based on the concepts of fuzzy set theory the approach uses a multicriteria decision making method to obtain the optimal strategy in the game a method which shows more advantages than the classical game methods moreover with this approach some useful conclusions are reached concerning the famous prisoner s dilemma problem in game theory

a lexicographical solution concept in an n person cooperative fuzzy game abstract in this paper a new solution concept in an n person cooperative fuzzy game with sidepayment is proposed we first define an excess with respect to a player in a fuzzy game with sidepayment usually the concept of an excess is defined for each coalition in contrast however we define an excess of a player by summing up all the excess of a coalition to which he belongs by considering a payoff vector which minimizes the excess of a player in the lexicographical order we proposed a new solution concept in a fuzzy game as well as in a nonfuzzy game then we further consider the problem to extend a nonfuzzy game into a fuzzy game such an extension can be described by the mappings from a characteristic function in a nonfuzzy game into a characteristic function in a fuzzy game an illustrative numerical example of the proposed solution concept to some extended fuzzy games is also presented