solving bimatrix games with fuzzy payoffs by introducing nature as a third player the paper elaborates on the fuzzy bimatrix games the payoffs are assumed to be fuzzy intervals with bounded support as defined by dubois and prade a new equilibrium concept is defined for this game by introducing nature as a third player and using a cuts sufficient conditions for its existence and a procedure for its computation are provided

entrywise relative perturbation bounds for exponentials of essentially non negative matrices a real square matrix is said to be essentially non negative if all of its off diagonal entries are non negative we establish entrywise relative perturbation bounds for the exponential of an essentially non negative matrix our bounds are sharp and contain a condition number that is intrinsic to the exponential function as an application we study sensitivity of continuous time markov chains

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

the randomization technique as a modeling tool and solution procedure for transient markov processes we present a randomization procedure for computing transient solutions to discrete state space continuous time markov processes this procedure computes transient state probabilities it is based on a construction relating a continuous time markov process to a discrete time markov chain modifications and extensions of the randomization method allow for computation of distributions of first passage times and sojourn times in markov processes and also the computation of expected cumulative occupancy times and expected number of events occurring during a time interval several implementations of the randomization procedure are discussed in particular we present an implementation for a general class of markov processes that can be described in terms of state space s event set e rate vectors r and target vectors t abbreviated as sert this general approach can handle systems whose state spaces are quite large if they have sparse generators

the pade method for computing the matrix exponential we analyze the pade method for computing the exponential of a real matrix more precisely we study the roundoff error introduced by the method in the general case and in three special cases 1 normal matrices 2 essentially nonnegative matrices aij 0 i j 3 matrices a such that a d 1 bd with d diagonal and b essentially nonnegative for these special matrices it turns out that the pade method is stable finally we compare the ward upper bound with our results and show that our bounds are generally tighter

max min solutions for fuzzy multiobjective matrix games abstract in this paper we consider two person zero sum games with fuzzy multiple payoff matrices we assume that each player has a fuzzy goal for each of the payoffs a degree of attainment of the fuzzy goal is defined and the max min strategy with respect to the degree of attainment of the fuzzy goal is examined if all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear the formulated mathematical programming problem which yields the max min strategy can be reduced to the linear programming problem by making use of sakawa s method the variable transformations and the relaxation procedure

games with fuzzy permission structure a conjunctive approach abstract a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take a permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others various assumptions can be made about how a permission structure affects the cooperation possibilities in the conjunctive approach it is assumed that each player needs permission from all his superiors this paper deals with fuzzy permission structures in the conjunctive approach in this model players could depend partially on other players that is they may have certain degree of autonomy first we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value finally we study a value for games with fuzzy permission structure which takes account of the indirect relations among players

computing exponentials of essentially non negative matrices entrywise to high relative accuracy a real square matrix is said to be essentially non negative if all of its off diagonal entries are non negative it has recently been shown that the exponential of an essentially non negative matrix is determined entrywise to high relative accuracy by its entries up to a condition number intrinsic to the exponential function numer math 110 2008 pp 393 403 thus the smaller entries of the exponential may be computed to the same relative accuracy as the bigger entries this paper develops algorithms to compute exponentials of essentially non negative matrices entrywise to high relative accuracy

subgraph centrality in complex networks we introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network smaller subgraphs are given more weight than larger ones which makes this measure appropriate for characterizing network motifs we show that the subgraph centrality c s i can be obtained mathematically from the spectra of the adjacency matrix of the network this measure is better able to discriminate the nodes of a network than alternate measures such as degree closeness betweenness and eigenvector centralities we study eight real world networks for which c s i displays useful and desirable properties such as clear ranking of nodes and scale free characteristics compared with the number of links per node the ranking introduced by c s i for the nodes in the protein interaction network of s cereviciae is more highly correlated with the lethality of individual proteins removed from the proteome

equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals when the game theory is applied to real world problems such as decision making in public and managerial problems on occasions it is difficult to assess payoffs exactly because of inaccuracy of information and fuzzy understanding of situations by experts in such cases games with fuzzy payoffs in which payoffs are represented as fuzzy numbers are often considered in this paper we consider equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs we introduce fuzzy goals for payoffs in order to incorporate ambiguity of a player s judgements and assume that the player tries to maximize degrees of attainment of the fuzzy goals the fuzzy goals for payoffs and the equilibrium solution with respect to the degree of attainment of the fuzzy goal are defined two basic methods one by weighting coefficients and the other by a minimum component are employed to aggregate multiple fuzzy goals when membership functions of fuzzy payoffs and fuzzy goals are all linear and the fuzzy decision in terms of the intersection is employed the necessary conditions that pairs of strategies be the equilibrium solutions is obtained when membership functions of fuzzy payoffs are quadratic functions those of fuzzy goals are linear and the fuzzy decision in terms of the convex combination is employed we also derive the necessary conditions that pairs of strategies be the equilibrium solutions

random payoff two person zero sum game with joint chance constraints abstract we study a two person zero sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability we prove that for the general random payoff zero sum game there exists a weak duality between the two formulations i e the optimal value of the minimizing player is an upper bound of the one of the maximizing player under certain assumptions we show that there also exists a strong duality where their optimal values are equal moreover we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed finally numerical examples are given to illustrate the performances of the proposed approaches

hausman tests for autocorrelation in the presence of lagged dependent variables some further results abstract further results on the augmented regression test are given a generalized augmented regression test a lagrange multiplier test and a new specification error test based upon locally equivalent alternatives are discussed in the context of testing for general order autocorrelation when there are several lagged values of the dependent variable in the regressors

componentwise accurate fluid queue computations using doubling algorithms markov modulated fluid queues are popular stochastic processes frequently used for modelling real life applications an important performance measure to evaluate in these applications is their steady state behaviour which is determined by the stationary density computing it requires solving a nonsymmetric m matrix algebraic riccati equation and indeed computing the stationary density is the most important application of this class of equations xue et al numer math 120 671 700 2012 provided a componentwise first order perturbation analysis of this equation proving that the solution can be computed to high relative accuracy even in the smallest entries and suggested several algorithms for computing it an important step in all proposed algorithms is using so called triplet representations which are special representations for m matrices that allow for a high accuracy variant of gaussian elimination the gth like algorithm however triplet representations for all the m matrices needed in the algorithm were not found explicitly this can lead to an accuracy loss that prevents the algorithms from converging in the componentwise sense in this paper we focus on the structured doubling algorithm the most efficient among the proposed methods in xue et al and build upon their results providing i explicit and cancellation free expressions for the needed triplet representations allowing the algorithm to be performed in a really cancellation free fashion ii an algorithm to evaluate the final part of the computation to obtain the stationary density and iii a componentwise error analysis for the resulting algorithm the first explicit one for this class of algorithms we also present numerical results to illustrate the accuracy advantage of our method over standard normwise accurate algorithms

myerson values for games with fuzzy communication structure in 1977 myerson considered cooperative games with communication structure a communication structure is an undirected graph describing the bilateral relationships among the players he introduced the concept of allocation rule for a game as a function obtaining an outcome for each communication structure among the players of the game the myerson value is a specific allocation rule extending the shapley value of the game more recently the authors studied games with fuzzy communication structures using fuzzy graph theoretic ideas now we propose a general framework in order to define fuzzy myerson values players in a coalition need to measure their profit using their real individual and communication capacities at every moment because these attributes are fuzzy when the game is proposed so they look for forming connected coalitions working at the same level the different ways to obtain these partitions by levels determine different myerson values for the game several interesting examples of these ways are studied in the paper following known models in games with fuzzy coalitions the proportional model and the choquet model

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

existence of equilibrium solution for a non cooperative game with fuzzy goals and parameters in this paper we introduce a concept of equilibrium for a non cooperative game with fuzzy goals involving fuzzy parameters this equilibrium is based on zimmermann s approach for solving linear multiobjective problems with fuzzy goals and the concept of n s equilibrium introduced by zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior we also provide a theorem of existence of this equilibrium based on the fan inequality

fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games recently the concept of classical bargaining set given by aumann and maschler in 1964 has been extended to fuzzy bargaining set in this paper we give a modification to correct some weakness of this extension we also extend the concept of the mas colell s bargaining set the other major type of bargaining sets to its corresponding fuzzy bargaining set our main effort is to prove existence theorems for these two types of fuzzy bargaining sets we will also give necessary and sufficient conditions for these bargaining sets to coincide with the aubin core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector we show that both aumann maschler and mas colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its aubin core

games with fuzzy authorization structure a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take it is often assumed that the players are free to participate in any coalition but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions those relationships must be taken into account if we want to distribute the profits fairly in this respect several models have been proposed in literature in all of them dependency relationships are considered to be complete in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all nevertheless in some situations it is possible to consider another option that a player has a degree of freedom to cooperate within a coalition a model for those situations is presented

nash equilibrium strategy for fuzzy non cooperative games in this article two person zero sum games are investigated in the fuzzy environment several models constructed by maeda in the symmetrical fuzzy environment are extended to the models in the asymmetric fuzzy environment the existence of equilibrium strategies for these extended models is proposed in the asymmetric fuzzy environment however in some cases nash equilibrium strategies may not exist therefore two special cases are presented for which nash equilibrium strategies do exist in order to investigate the existence of weak pareto nash equilibrium strategies for fuzzy matrix games we introduce the concept of crisp bi matrix games with parameters by solving the parametric bi matrix games we obtain the weak pareto nash equilibrium strategies for the fuzzy matrix games

communicability in complex networks we propose a new measure of the communicability of a complex network which is a broad generalization of the concept of the shortest path according to the new measure most of the real world networks display the largest communicability between the most connected popular nodes of the network assortative communicability there are also several networks with the disassortative communicability where the most popular nodes communicate very poorly to each other using this information we classify a diverse set of real world complex systems into a small number of universality classes based on their structure dynamic correlation in addition the new communicability measure is able to distinguish finer structures of networks such as communities into which a network is divided a community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network

pade approximation for the exponential of a block triangular matrix abstract in this work we obtain improved error bounds for pade approximations to e a when a is block triangular as a result improved scaling strategies ensue which avoid some common overscaling difficulties

linear production games with fuzzy control the aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options in order to model these situations we consider several kinds of fuzzy controls which can be modelled as different simple fuzzy games an lp game which is an extension of lp games with committee control introduced in curiel et al on balanced games and games with committee control or spectrum 11 1989 83 88 is obtained and its core is studied

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

a fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers the aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers tfns which are arbitrary in this method it always assures that players gain floor and loss ceiling have a common tfn type fuzzy value and hereby any matrix game with payoffs of tfns has a tfn type fuzzy value based on duality theorem of linear programming lp and the representation theorem for fuzzy sets the mean and the lower and upper limits of the tfn type fuzzy value are easily computed through solving the derived lp models with data taken from 1 cut set and 0 cut set of fuzzy payoffs hereby the tfn type fuzzy value of any matrix game with payoffs of tfns can be explicitly obtained moreover we can easily compute the upper and lower bounds of any alfa cut set of the tfn type fuzzy value for any matrix game with payoffs of tfns and players optimal mixed strategies through solving the derived lp models at any specified confidence level alfa the proposed method in this paper is demonstrated with a numerical example and compared with other methods to show the validity applicability and superiority

quadrature rule based bounds for functions of adjacency matrices bounds for entries of matrix functions based on gauss type quadrature rules are applied to adjacency matrices associated with graphs this technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities estrada index subgraph centrality communicability that describe properties of networks

heterogeneous treatment effects instrumental variables without monotonicity imbens and angrist 1994 were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables more recently heckman and vytlacil 1999 suggested the estimation of a variety of treatment effect parameters using a local version of their approach we investigate the sensitivity of the respective estimates to random departures from monotonicity approximations to the respective bias terms are derived in an empirical application the bias is calculated and bias corrected estimates are obtained the accuracy of the approximation is investigated in a monte carlo study

fuzzy linear programming models to solve fuzzy matrix games abstract in this paper a zero sum two person game with imprecise values in its matrix of payoffs is considered we propose a method for its solution based on the establishment of a fuzzy linear programming f l p problem for each player the method is shown as a generalization of that conventionally used in the solution of a classical game to solve such f l p problems we propose the auxiliary models resulting from the application of some of the methods for ranking fuzzy numbers hence according to the kind of ranking method that players want to use different solutions to the former game can be obtained we show that these solutions are of the same nature as the parameters defining the game and corresponding to a fuzzy predicate that can be established as the value of the game is around

optimal solutions for group matrix games involving interval valued fuzzy numbers abstract traditional games theory is based on the idea of having a set of deterministic payoffs to represent actions taken by homogeneous individuals interaction among players while in several real scenarios social and business conflicts are handled by groups of actors with different technical social skills this way a group game problem can be seen as to two groups of players who individually select a strategy to win so the information given by every player in their group affects the payoffs of such game sometimes deterministic payoffs are not available and even when they can be obtained from negotiation between players they are not clearly defined indeed within groups individual players could have different perceptions of the payoffs for which we propose a uncertain based matrix games model involving interval valued fuzzy payoffs

solving constrained matrix games with payoffs of triangular fuzzy numbers constrained matrix games with payoffs of triangular fuzzy numbers tfns are a type of matrix games with payoffs expressed by tfns and sets of players strategies which are constrained so far as we know no study have yet been attempted for constrained matrix games with payoffs of tfns since there is no effective way to simultaneously incorporate the payoffs fuzziness and strategies constraints into classical and or fuzzy matrix game methods the aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of tfns in this methodology we introduce the concepts of alpha constrained matrix games for constrained matrix games with payoffs of tfns and the values by the duality theorem of linear programming it is proven that players gain floor and loss ceiling always have a common interval type value and hereby any alpha constrained matrix game has an interval type value moreover using the representation theorem for the fuzzy set it is proven that any constrained matrix game with payoffs of tfns always has a tfn type fuzzy value the auxiliary linear programming models are derived to compute the lower and upper bounds of the interval type value and optimal strategies of players for any alpha constrained matrix game in particular the mean and the lower and upper limits of the tfn type fuzzy value of any constrained matrix game with payoffs of tfns can be directly obtained through solving the derived three linear programming models with data taken from only 1 cut and 0 cut of payoffs hereby the tfn type fuzzy value of any constrained matrix game with payoffs of tfns are easily computed the proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example

characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff in this paper we consider fuzzy bimatrix games which mean bimatrix games with fuzzy payoff matrices we define two types of concepts of equilibrium strategy and investigate their relationships moreover we prove that these nash equilibrium strategies exist in any fuzzy bimatrix games

accurate computation of the smallest eigenvalue of a diagonally dominant m matrix if each off diagonal entry and the sum of each row of a diagonally dominant m matrix are known to certain relative accuracy then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers in this paper we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms

a note on the core minimal conversely consistent enlargement abstract the moulin reduction is extended by reducing the number of the players to the framework of fuzzy games based on this extended moulin reduction the axiomatic result of the core in tadenuma s 25 case does not hold in the context of fuzzy games and the core also violates the converse consistency therefore we propose the minimal core which possesses the converse consistency and is also the smallest solution satisfying the core

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

full versus limited information estimation of a rational expectations model some numerical comparisons abstract this paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques a a limited information one which uses instrumental variables to estimate a single equation hansen and singleton 1982 and b a full information one which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations hansen and sargent 1980 the paper compares the two with respect to both 1 asymptotic efficiency under the null hypothesis of no misspecification and 2 asymptotic bias and power in the presence of certain local alternatives it is found that 1 full information standard errors are only moderately smaller than limited information standard errors and 2 when the model is misspecified full information tests tend to be more powerful and its parameter estimates tend to be more biased this suggests that at least in the model considered here the gains from the use of the less robust and computationally more complex full information technique are not particularly large

local asymptotic specification error analysis an approximation to the inconsistency introduced by imposing an incorrect restriction on a parametric model is given the approximation can be applied to estimators generated by optimizing any objective function satisfying certain regularity conditions examples given include analysis of misspecification in discrete choice and time series models estimated by maximum likelihood and in a nonlinear regression model specification error analysis in the linear regression model has been studied by theil 1 who gives formulas for e g the effect of leaving out relevant variables on the expected values of the estimators of the coefficients of the included variables in this paper we suggest analogous formulas for estimators obtained by optimizing an objective function subject to restrictions we have in mind maximizing 1 n x loglikelihood and will usually use this terminology we consider the effect on the limit of the restricted estimator of a small violation of the restrictions in the linear regression case our formula coincides with that given by theil in order to keep our results widely applicable and to avoid a mass of unnecessary detail we make assumptions on the asymptotic behavior of the loglikelihood function itself rather than on the data generating process per se many alternative sets of assumptions on the data densities can lead to the behavior we require of the loglikelihood functions these will not be pursued here the interested reader is referred to e g white 12 for the case of independent observations and kohn 8 for the time series case 1 general formulas the general approach we take is based on a linear approximation to the likelihood function at the maximum likelihood estimator it is in this sense that our analysis is local for some models the local and global specification error results coincide a well known case is the effect of omitted regressors in the linear regression model essentially the only cases involve linearity although often there is agreement regarding the signs of the inconsistency we show below that the local and global results even fail to coincide in the case of misspecified ar processes generally however the global results are unknown 2 taylor expansions are typically used together with assumptions on the data generating process to obtain the asymptotic distribution of the maximum likelihood estimator cramer 3 in this paper we will not concern ourselves with asymptotic distributions of vn normed mle s since these have been worked

communicability betweenness in complex networks abstract betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks they allow us to study the extent to which a node takes part when information is passed around the network nodes with high betweenness may be regarded as key players that have a highly active role at one extreme betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes at the other extreme an alternative type of betweenness has been defined by considering all possible walks of any length in this work we propose a betweenness measure that lies between these two opposing viewpoints we allow information to pass through all possible routes but introduce a scaling so that longer walks carry less importance this new definition shares a similar philosophy to that of communicability for pairs of nodes in a network which was introduced by estrada and hatano e estrada n hatano phys rev e 77 2008 036111 having defined this new communicability betweenness measure we show that it can be characterized neatly in terms of the exponential of the adjacency matrix we also show that this measure is closely related to a frechet derivative of the matrix exponential this allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations using illustrative synthetic and real life networks we show that the new betweenness measure behaves differently to existing versions and in particular we show that it recovers meaningful biological information from a protein protein interaction network

on characterization of equilibrium strategy of two person zero sum games with fuzzy payoffs in this paper we consider fuzzy matrix games namely two person zero sum games with fuzzy payoffs based on fuzzy max order for such games we define three kinds of concepts of minimax equilibrium strategies and investigate their properties first we shall show that these equilibrium strategies are characterized as nash equilibrium strategies of a family of parametric bi matrix games with crisp payoffs second we investigate properties of values of fuzzy matrix games by means of possibility and necessity measures in addition we give a numerical example to illustrate utility of our approaches

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

on the use of the ranking function approach to solve fuzzy matrix games in a direct way abstract a general method of solving fuzzy matrix games is presented this method is suitable when players choose their fuzzy number ranking procedures in a wide class i e that which may be represented by means of a linear ranking functions in the first case described both players use the same criterion to rank fuzzy numbers and in the second case each player uses different criteria several situations of players knowledge are analyzed in the second case and game solutions are provided in all of them

duality in linear programming with fuzzy parameters and matrix games with fuzzy pay offs abstract a dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay offs is equivalent to a primal dual pair of such fuzzy linear programming problems further certain difficulties with similar studies reported in the literature are discussed

matrix games with payoffs of belief structures imprecise matrix games such as interval valued matrix games and fuzzy matrix games have attracted much interest for a long time most of the previous studies on imprecise matrix games mainly focus on the fuzzy uncertainty of payoffs however the uncertainties of nonspecificity and discord involved in payoffs are not well addressed so far the purpose of this paper is to study the matrix game with such types of uncertainties in order to achieve that purpose we present a matrix game model with payoffs of belief structures so as to integrate discord and nonspecificity the proposed model can be used to express more imprecise interactions between players in the reality besides as another main contribution of the study an effective method for solving matrix games with belief structures payoffs is developed to help us find the equilibrium points of the kind of games at last an example is given to illustrate the proposed model and method

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

non cooperative fuzzy games in normal form a survey in this paper we present a review of most of the approaches for solving non cooperative fuzzy games in normal form applications of these games are reviewed as well we also present a new class of fuzzy games in normal form the class of non cooperative games involving fuzzy parameters finally some potential directions of research are provided throughout the paper and in the conclusion

cooperative fuzzy games we derive versions of known results dealing with core equilibria and shapley values of cooperative games in the case of cooperative fuzzy games i e games defined on fuzzy subsets of the set of n players a fuzzy coalition is an n vector i associating with each player i his rate of participation i 0 1 in the fuzzy coalition and the real number v is the coalition worth assumed to be positively homogeneous if also v is superadditive or equivalently concave the fuzzy game with side payments has a nonempty core associated with the coalition worth function for any ordinary game with side payments is a fuzzy extension thereof viz the fuzzy game whose coalition worth function is the least positively homogeneous superadditive function majorizing the coalition worth function of the original game the fuzzy extension always has a nonempty core moreover if the original game has a nonempty core it coincides with that of its fuzzy extension analogous results are established for games without side payments an axiomatization of values of fuzzy games with side payments is also given the results are applied to show that the set of walras equilibria coincides with the fuzzy core of an economy

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

pareto optimal security strategies in matrix games with fuzzy payoffs we present a new methodology for the analysis of fuzzy payoff matrix games the main difficulty that appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are fuzzy quantities our approach does not transform the fuzzy payoffs to crisp numbers via standard defuzzyfication but we use standard fuzzy orders which allows us to find solutions within the same space of fuzzy numbers moreover we provide a method to solve these games finding equivalent fuzzy linear programs whose maximal solutions give the solutions of the games

cores of fuzzy games and their convexity in this paper the proper core and dominance core of a fuzzy game are introduced to guarantee equality between the proper core and the dominance core some mild conditions are provided another important issue for the convexity of the dominance core is also addressed

the cournot game under a fuzzy decision environment the conventional precision based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist this paper considers the cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers our model utilizes the weighted center of gravity wcog method to defuzzify the fuzzy profit function into a crisp value we derive the equilibrium cournot quantity of each firm by simultaneously solving the first order condition of each firm our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method in addition we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm s cost and market demand functions we conduct sensitivity analysis to investigate the effect of parameter perturbations on firms outcomes the results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters

nontransferable utility games with fuzzy coalition restrictions abstract a value for nontransferable utility ntu games with fuzzy coalition restrictions is introduced and characterized in a similar way as the shapley value for transferable utility tu games has been extended in the literature to study games with restricted cooperation we extend the shapley ntu value to deal with ntu games in situations in which there are fuzzy dependency relationships among the players

existence of fuzzy prekernels and mas colell bargaining sets in tu games abstract in this paper we first prove the existence of fuzzy prekernels and fuzzy nucleolus in tu fuzzy games which generalize the corresponding results for classical tu games as an application we apply the existence of fuzzy prekernels to derive an existence theorem for mas colell fuzzy bargaining sets and a stronger existence theorem for mas colell bargaining sets than the one by vohra 1991 18 we also provide an axiomatization theorem for fuzzy prekernels

feasibility and pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters abstract in this paper we focus on multiobjective nonlinear programming problems with fuzzy parameters and extend the ordinary feasibility and pareto optimality concepts based on the concepts of possibility and necessity for fuzzy numbers using the four indices for ranking two fuzzy numbers four types of feasibility and pareto optimality are defined and the relationships among them are examined in detail these concepts can be viewed as quite generalized versions of the well known feasibility and pareto optimality concepts and the generalized pareto optimal solutions for the multiobjective nonlinear programming problems with fuzzy parameters may be obtained on the basis of the method of nonlinear programming

two person zero sum game approach for fuzzy multiple attribute decision making problems the multiple attribute decision making madm problem deals with candidate priority alternatives with respect to various attributes madm techniques are popularly used in diverse fields such as engineering economics management science transportation planning etc several approaches have been developed for assessing the weights of madm problems e g the eigenvector method electre topsis etc in this paper we obtained weights of a madm problem with a fuzzy decision matrix by formulating it as a two person zero sum game with an uncertain payoff matrix moreover the equilibrium solution and the resolution method for the madm game have also been developed these results are validated by a product development example of nano materials our study is an innovative approach for applying the game theory on madm problems with management of technology mot

full versus limited information estimation of a rational expectations model this paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques a a limited information one which uses instrumental variables to estimate a single equation hansen and singleton 1982 and b a full information one which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations hansen and sargent 1980 the paper compares the two with respect to both 1 asymptotic efficiency under the null hypothesis of no misspecification and 2 asymptotic bias and power in the presence of certain local alternatives it is found that 1 full information standard errors are only moderately smaller than limited information standard errors and 2 when the model is misspecified full information tests tend to be more powerful and its parameter estimates tend to be more biased this suggests that at least in the model considered here the gains from the use of the less robust and computationally more complex full information technique are not particularly large

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

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

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

computing the exponential of large block triangular block toeplitz matrices encountered in fluid queues the erlangian approximation of markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block triangular block toeplitz structure to this end we propose some algorithms which exploit the toeplitz structure and the properties of generators such algorithms allow us to compute the exponential of very large matrices which would otherwise be untreatable with standard methods we also prove interesting decay properties of the exponential of a generator having a block triangular block toeplitz structure