coreness of cooperative games with truncated submodular profit functions coreness represents solution concepts related to core in cooperative games which captures the stability of players motivated by the scale effect in social networks economics and other scenario we study the coreness of cooperative game with truncated submodular profit functions specifically the profit function f cdot is defined by a truncation of a submodular function sigma cdot f cdot sigma cdot if sigma cdot ge eta and f cdot 0 otherwise where eta is a given threshold in this paper we study the core and three core related concepts of truncated submodular profit cooperative game we first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty when core is empty we show hardness results and approximation algorithms for computing other core related concepts including relative least core value absolute least core value and least average dissatisfaction value

semilinear elliptic equations on unbounded domains on presente une nouvelle approche variationnelle a l existence des solutions pour le probleme aux valeurs limites u u r x f u x x x h 0 1 sur des domaines non bornes

complementary cooperation minimal winning coalitions and power indices we introduce a new simple game which is referred to as the complementary weighted multiple majority game c wmmg for short c wmmg models a basic cooperation rule the complementary cooperation rule and can be taken as a sister model of the famous weighted majority game wmg for short in c wmmg each player is characterized by a nonnegative vector with a fixed dimension and players in the same coalition cooperate by producing a characteristic vector for this coalition each dimension of this vector equals the maximum of the corresponding dimensions of its members the value of a coalition is 1 if and only if the sum of its characteristic vector is larger than that of its complementary coalition in which case the coalition is called winning otherwise the coalitional value is 0 in this paper we concentrate on the two dimensional c wmmg an interesting property of this case is that there are at most n 1 minimal winning coalitions mwcs for short and they can be enumerated in time o nlogn where n is the number of players this property guarantees that the two dimensional c wmmg is more handleable than wmg in particular we prove that the main power indices i e the shapley shubik index the penrose banzhaf index the holler packel index and the deegan packel index are all polynomially computable to make a comparison with wmg we know that it may have exponentially many mwcs and none of the four power indices is polynomially computable unless p np still for the two dimensional case we show that local monotonicity holds for all of the four power indices in wmg this property is possessed by the shapley shubik index and the penrose banzhaf index but not by the holler packel index or the deegan packel index since our model fits very well the cooperation and competition in team sports we hope that it can be potentially applied in measuring the values of players in team sports say help people give more objective ranking of nba players and select mvps and consequently bring new insights into contest theory and the more general field of sports economics it may also provide some interesting enlightenments into the design of non additive voting mechanisms last but not least the threshold version of c wmmg is a generalization of wmg and natural variants of it are closely related with the famous airport game and the stable marriage roommates problem

reasoning about coalitional games we develop investigate and compare two logic based knowledge representation formalisms for reasoning about coalitional games the main constructs of coalitional game logic cgl are expressions for representing the ability of coalitions which may be combined with expressions for representing the preferences that agents have over outcomes modal coalitional game logic mcgl is a normal modal logic in which the main construct is a modality for expressing the preferences of groups of agents for both frameworks we give complete axiomatisations and show how they can be used to characterise solution concepts for coalitional games we show that while cgl is more expressive than mcgl the former can only be used to reason about coalitional games with finitely many outcomes while mcgl can be used to reason also about games with infinitely many outcomes and is in addition more succinct we characterise the computational complexity of satisfiability for cgl and give a tableaux based decision procedure

matching games the least core and the nucleolus a matching game is a cooperative game defined by a graph g n e the player set is n and the value of a coalition s n is defined as the size of a maximum matching in the subgraph induced by s we show that the nucleolus of such games can be computed efficiently the result is based on an alternative characterization of the least core which may be of independent interest the general case of weighted matching games remains unsolved

on the solvability of a semilinear operator equation at resonance as applied to elliptic boundary value problems in unbounded domains on considere la resolubilite faible de problemes aux valeurs limites elliptiques semi lineaires sur un domaine non borne g r n sous forme d une equation operateur au bu ou a l 2 g 74dom a l 2 g est lineaire et autoadjoint avec dom a w m 2 g m 2 continument plonge et b w m 1 2 g l 2 g est un operateur de substitution induit par une fonction de caratheodory avec au plus une croissance lineaire

generalization of fredholm alternative for nonlinear differential operators on considere le probleme aux valeurs limites u t p 2 u t f t u t g t t 0 u 0 u 0 on demontre que si lim u inf f t u u p 2 u lim u sup f t u u p 2 u sont entre des valeurs propres du probleme aux valeurs propres u p 2 u u p 2 u sur 0 u 0 u 0 alors le probleme aux limites est resoluble pour tout g l 1

resonance and rotation numbers for planar hamiltonian systems multiplicity results via the poincare birkhoff theorem abstract in the general setting of a planar first order system 0 1 u g t u u r 2 with g 0 t r 2 r 2 we study the relationships between some classical nonresonance conditions including the landesman lazer one at infinity and in the unforced case i e g t 0 0 at zero and the rotation numbers of large and small solutions of 0 1 respectively such estimates are then used to establish via the poincare birkhoff fixed point theorem new multiplicity results for t periodic solutions of unforced planar hamiltonian systems j u u h t u and unforced undamped scalar second order equations x g t x 0 in particular by means of the landesman lazer condition we obtain sharp conclusions when the system is resonant at infinity

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

core stability of minimum coloring games in cooperative game theory a characterization of games with stable cores is known as one of the most notorious open problems we study this problem for a special case of the minimum coloring games introduced by deng et al 1999 which arise from a cost allocation problem when the players are involved in conflict in this paper we show that the minimum coloring game on a perfect graph has a stable core if and only if every vertex of the graph belongs to a maximum clique we also consider the problem on the core largeness the extendability and the exactness of minimum coloring games as a consequence we show that it is conp complete to decide whether a given game has a large core is extendable or is exact

nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems this paper deals with the solvability of the nonlinear operator equations in normed spaces yx egx j where dp is a linear map with possible nontrivial kernel applications are given to the existence of periodic solutions for the thirdorder scalar differential equation x ax bx cx g t x p t under various conditions on the interaction of g t x x with spectral contigurations of a b and c

existence and uniqueness of periodic solution for a class of semilinear evolution equations this paper deals with the existence and uniqueness for the periodic boundary value problem of the semilinear evolution equation in a hilbert space h u t au t f t u t 0 t u 0 u where a d a h h is a positive definite self adjoint operator 0 and f 0 h h satisfy caratheodory condition we present some spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions are the generalization for nonresonance condition of the self adjoint elliptic boundary value problems

coalitions among computationally bounded agents abstract this paper analyzes coalitions among self interested agents that need to solve combinatorial optimization problems to operate efficiently in the world by colluding coordinating their actions by solving a joint optimization problem the agents can sometimes save costs compared to operating individually a model of bounded rationality is adopted where computation resources are costly it is not worthwhile solving the problems optimally solution quality is decision theoretically traded off against computation cost a normative application and protocol independent theory of coalitions among bounded rational agents is devised the optimal coalition structure and its stability are significantly affected by the agents algorithms performance profiles and the cost of computation this relationship is first analyzed theoretically then a domain classification including rational and bounded rational agents is introduced experimental results are presented in vehicle routing with real data from five dispatch centers this problem is np complete and the instances are so large that with current technology any agent s rationality is bounded by computational complexity

nonresonance semilinear operator equations in unbounded domains on considere le probleme de dirichlet pour l equation lu g x u u u h x y u ou l est un operateur uniformement elliptique de dom l h 01 h 2 g r u 1 r et h r n 1 r avec h borne telle que n g x s n 1 pour tout s r n 1 et p p x et sont deux constantes et 1 2 3 sont les valeurs propres de l on demontre l existence d une solution pour un domaine r n non borne

solving coalitional resource games coalitional resource games crgs are a form of non transferable utility ntu game which provide a natural formal framework for modelling scenarios in which agents must pool scarce resources in order to achieve mutually satisfying sets of goals although a number of computational questions surrounding crgs have been studied there has to date been no attempt to develop solution concepts for crgs or techniques for constructing solutions in this paper we rectify this omission following a review of the crg framework and a discussion of related work we formalise notions of coalition structures and the core for crgs and investigate the complexity of questions such as determining nonemptiness of the core we show that while such questions are in general computationally hard it is possible to check the stability of a coalition structure in time exponential in the number of goals in the system but polynomial in the number of agents and resources as a consequence checking stability is feasible for systems with small or bounded numbers of goals we then consider constructive approaches to generating coalition structures we present a negotiation protocol for crgs give an associated negotiation strategy and prove that this strategy forms a subgame perfect equilibrium we then show that coalition structures produced by the protocol satisfy several desirable properties pareto optimality dummy player and pseudo symmetry

computing the least core and nucleolus for threshold cardinality matching games cooperative games provide a framework for fair and stable profit allocation in multi agent systems core least core and nucleolus are such solution concepts that characterize stability of cooperation in this paper we study the algorithmic issues of the least core and nucleolus of threshold cardinality matching games tcmg a tcmg is defined on a graph g v e and a threshold t in which the player set is v and the profit of a coalition s v is 1 if the size of a maximum matching in g s meets or exceeds t and 0 otherwise we first show that for a tcmg the problems of computing least core value finding and verifying least core payoff are all polynomial time solvable we also provide a general characterization of the least core for a large class of tcmg cf theorem 2 next based on gallai edmonds decomposition in matching theory we establish a concise formulation of the nucleolus for a special case of tcmg when the threshold t equals 1 for arbitrary t we prove that the nucleolus of tcmg can be obtained in polynomial time for bipartite graphs and graphs with a perfect matching for a tcmg the problems of computing least core value finding and verifying least core payoff are polynomial time solvable we provide a general characterization of the least core for a large class of tcmg we establish a concise formulation of the nucleolus for a typical case of tcmg when the threshold t equals 1 for an arbitrary threshold t the nucleolus of tcmg can be obtained in polynomial time for graphs with a perfect matching for an arbitrary threshold t the nucleolus of tcmg can be obtained in polynomial time for bipartite graphs

cooperation through social influence abstract we consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents we model this scenario by an influence game a cooperative simple game in which a team or coalition of players succeeds if it is able to convince enough agents to participate in the task to vote in favor of a decision we take the linear threshold model as the influence model we show first the expressiveness of influence games showing that they capture the class of simple games then we characterize the computational complexity of various problems on influence games including measures length and width values shapley shubik and banzhaf and properties of teams and players finally we analyze those problems for some particular extremal cases with respect to the propagation of influence showing tighter complexity characterizations

complexity of the minimum base game on matroids this paper studies the complexity of computing solution concepts for a cooperative game called the minimum base game mbg e c where its characteristic function c 2e is defined as c s the weight w b of a minimum weighted base b s for a given matroid m e and a weight function w e the minimum base game contains as a special case the minimum spanning tree game mstg in an edge weighted graph in which players are located on the edges by interpreting solution concepts of games such as core value and shapley value in terms of matroid theory we obtain the core of mbg is nonempty if and only if the matroid m has no circuit consisting only of edges with negative weights checking the concavity and subadditivity of an mbg can be done in oracle polynomial time the value of an mbg exists if and only if the core is not empty the value of mstg can be computed in polynomial time while there is no oracle polynomial algorithm for a general mbg computing the shapley value

on the complexity of cooperative solution concepts we study from a complexity theoretic standpoint the various solution concepts arising in cooperative game theory we use as a vehicle for this study a game in which the players are nodes of a graph with weights on the edges and the value of a coalition is determined by the total weight of the edges contained in it the shapley value is always easy to compute the core is easy to characterize when the game is convex and is intractable np complete otherwise similar results are shown for the kernel the nucleolus the e core and the bargaining set as for the von neumann morgenstern solution we point out that its existence may not even be decidable many of these results generalize to the case in which the game is presented by a hypergraph with edges of size k 2

periodic solutions for some nonlinear differential equations of neutral type where f ir x ir ir is a caratheodory function f x is 2n periodic for every x ci e r and r e io 2n this problem has been studied by sadovskii in 151 by hale and mawhin in 6 in the case ial 1 to the previous one our interest is particularly motivated by the fact that represents a simple and meaningful model for a general phenomenon which often arises in the study of functional differential equations in fact as is well known in some cases a delayed differential equation can be seen as a perturbation of an ordinary differential equation in particular this occurs when the delayed term in the equation can be considered smaller than the ordinary one or dominated by it when such domination is available many good properties can be proved and several results such as those of 6 and 16 take advantage of this fact on the contrary when no domination is present the situation is much more complicated and in general very little is known in problem the delayed term can be considered dominated by the ordinary one whenever ial 1 as a matter of fact in this case one can prove the invertibility of the differential operator l x x a r ux the compactness of its inverse and even some a priori estimates for the solutions consequently one can reduce to a fixed point problem and solve it by means of some topological degree argument however when 11 1 so that the weight of the two terms x t and x t t is the same the above properties fail and moreover for some delays the kernel of the differential operator lx x a r is infinite dimensional therefore one must look for different methods problem is thus a simple but nevertheless significant example of the considerations illustrated by hale in 5 about the difficulty of undertaking a unified approach in the study of functional differential equations at the same time it provides an analogy between neutral equations and the wave equation in the line suggested by hale in 5

doubly resonant semilinear elliptic problems via nonsmooth critical point theory abstract we consider the existence of weak solutions for classical doubly resonant semilinear elliptic problems we show how the main technical assumptions can be used to define appropriate metrics on the underlying function space so that extensions of the results already known in the literature can be obtained using only basic facts from critical point theory for continuous functionals on complete metric spaces

the composition factors of the functor of permutation modules the grothendieck group of permutation modules for a finite group g becomes a biset functor when g is allowed to vary all the composition factors of this biset functor are determined

a linear approximation method for the shapley value the shapley value is a key solution concept for coalitional games in general and voting games in particular its main advantage is that it provides a unique and fair solution but its main drawback is the complexity of computing it e g for voting games this complexity is p complete however given the importance of the shapley value and voting games a number of approximation methods have been developed to overcome this complexity among these owen s multi linear extension method is the most time efficient being linear in the number of players now in addition to speed the other key criterion for an approximation algorithm is its approximation error on this dimension the multi linear extension method is less impressive against this background this paper presents a new approximation algorithm based on randomization for computing the shapley value of voting games this method has time complexity linear in the number of players but has an approximation error that is on average lower than owen s in addition to this comparative study we empirically evaluate the error for our method and show how the different parameters of the voting game affect it specifically we show the following effects first as the number of players in a voting game increases the average percentage error decreases second as the quota increases the average percentage error decreases third the error is different for players with different weights players with weight closer to the mean weight have a lower error than those with weight further away we then extend our approximation to the more general k majority voting games and show that for n players the method has time complexity o k 2n and the upper bound on its approximation error is o k 2 n

existence of critical point for abstract resonant problems with unbounded nonlinearities and applications to differential equations abstract in this paper using well known variational methods we prove a general abstract theorem on the existence of a critical point for resonant problems with unbounded nonlinearities and then apply it to ordinary and partial differential equations with generalized ahmad lazer paul conditions the abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations

coalition structure generation with worst case guarantees coalition formation is a key topic in multiagent systems one may prefer a coalition structure that maximizes the sum of the values of the coalitions but often the number of coalition structures is too large to allow exhaustive search for the optimal one furthermore finding the optimal coalition structure is np complete but then can the coalition structure found via a partial search be guaranteed to be within a bound from optimum we show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound we present an algorithm that establishes a tight bound within this minimal amount of search and show that any other algorithm would have to search strictly more the fraction of nodes needed to be searched approaches zero as the number of agents grows if additional time remains our anytime algorithm searches further and establishes a progressively lower tight bound surprisingly just searching one more node drops the bound in half as desired our algorithm lowers the bound rapidly early on and exhibits diminishing returns to computation it also significantly outperforms its obvious contenders finally we show how to distribute the desired search across self interested manipulative agents 1999 elsevier science b v all rights reserved

finite rationality and interpersonal complexity in repeated games a measure of complexity for repeated game strategies is studied this measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting specifically the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set i e the number of distinct strategies induced by the original strategy in all possible subgames we observe that this cardinality is equal to the size cardinality of the state set of the smallest automaton which can implement the strategy thus in a sense complexity is measured on the basis of the amount of computing power inherent in the strategy a measure of strategic memory is also studied the following results are obtained 1 combining two notions of bounded rationality epsilon equilibrium and finite complexity we find that every subgame perfect equilibrium of the repeated game can be approximated with regard to payoffs by a subgame perfect epsilon equilibrium of finite complexity 2 for a generic class of normal form stage games at every discount robust subgame perfect drsp equilibrium there are necessary relationships among the complexities and memories of the players strategies in the two player case strategies must be equally complex and must have equal memories 3 for a second class of two pla yer stage games we show that the payoff vectors for all drsp equilibria are obtainable via equilibria in which the players strategies are equally complex and have equal memoiies

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

semilinear second order evolution equations of compact type with regular boundary conditions on etablit l existence de solutions au sens faible de x a b t x x x f t x x i1 x 0 i2 x 0 i1 x t i2 x t 0 i 1 2 dans un espace de hilbert h ou t j 0 t ij b ij c

on bouc s and thevenaz s conjectures on b groups abstract bouc proposed the following conjecture a finite group g is nilpotent if and only if its largest quotient b group g is nilpotent and thevenaz proposed another conjecture a finite group g is solvable if and only if its largest quotient b group g is solvable bouc has proven that his conjecture holds when g is solvable in this paper we consider some cases when g is not solvable let s be a nonabelian simple group except the chevalley groups a n q d n q e 6 q and a n 2 q if the group g has exactly one composition factor isomorphic to s then g is not solvable of course is not nilpotent that means we prove the conjectures in these cases

a conjecture on b groups in this note i propose the following conjecture a finite group g is nilpotent if and only if its largest quotient b group beta g is nilpotent i give a proof of this conjecture under the additional assumption that g be solvable i also show that this conjecture is equivalent to the following the kernel of restrictions to nilpotent subgroups is a biset subfunctor of the burnside functor

on the computational complexity of coalitional resource games we study coalitional resource games crgs a variation of qualitative coalitional games qcgs in which each agent is endowed with a set of resources and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources we investigate and classify the computational complexity of a number of natural decision problems for crgs over and above those previously investigated for qcgs in general for example we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound i e a limit value for every resource is co np complete we then investigate the relationship between crgs and qcgs and in particular the extent to which it is possible to translate between the two models we first characterise the complexity of determining equivalence between crgs and qcgs we then show that it is always possible to translate any given crg into a succinct equivalent qcg and that it is not always possible to translate a qcg into an equivalent crg we establish some necessary and some sufficient conditions for a translation from qcgs to crgs to be possible and show that even where an equivalent crg exists it may have size exponential in the number of goals and agents of its source qcg

internal structure of coalitions in competitive and altruistic graphical coalitional games this paper introduces a certain graphical coalitional game where the internal topology of the coalition depends on a prescribed communication graph structure among the agents the game value function is required to satisfy four axioms of value these axioms make it possible to provide a refined study of coalition structures on graphs by defining a formal graphical game and by assigning a positional advantage based on the shapley value to each agent in a coalition based on its connectivity properties within the graph using the axioms of value the graphical coalitional game can be shown to satisfy properties such as convexity fairness cohesiveness and full cooperativeness three measures of the contributions of agents to a coalition are introduced marginal contribution competitive contribution and altruistic contribution the mathematical framework given here is used to establish results regarding the dependence of these three types of contributions on the graph topology and changes in these contributions due to changes in graph topology based on these different contributions three online sequential decision games are defined on top of the graphical coalitional game and the stable graphs under each of these sequential decision games are studied it is shown that the stable graphs under the objective of maximizing the marginal contribution are any connected graph the stable graphs under the objective of maximizing the competitive contribution are the complete graph the stable graphs under the objective of maximizing the altruistic contribution are any tree

a semilinear problem with jumping nonlinearities in unbounded domains on considere des equations semi lineaires de la forme lu g x u f x ou r 2 l est un operateur autoadjoint dans l 2 g r r est une fonction de caratheodory et f l 2 on etudie le cas ou l n a pas de resolvante compacte et la non linearite g x u a au plus une croissance lineaire en u