an infinite dimensional purification principle without saturation abstract we establish a purification process for the min expected utilities coming from economy theory involved in the phenomenon of aversion to the ambiguity in game and decision theories we use instead of the saturation property a characterization of lyapunov infinite dimensional vector measures established in g knowles lyapunov vector measures siam j control 13 1975 294 303

metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

distributional strategies for games with incomplete information we study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game theoretic models using the notion of distributional strategies we prove four main theorems i a mixed strategy nash equilibrium existence theorem ii a pure strategy equilibrium existence theorem iii a pure strategy equilibrium existence theorem and iv a theorem describing how the set of equilibria of a game varies with the parameters of the game

communication and equilibrium in discontinuous games of incomplete information this paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs typically the discontinuities arise from indeterminacies ties in the underlying problem the point of view taken here is that the tie breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model a solution is therefore a tie breaking rule together with strategies satisfying the usual best response criterion when information is incomplete solutions need not exist that is there may be no tie breaking rule that is compatible with the existence of strategy profiles satisfying the usual best response criteria it is shown that the introduction of incentive compatible communication cheap talk restores existence

a compartmental model for computer virus propagation with kill signals research in the area of kill signals for prevention of computer virus is of significant importance for computer users the kill signals allow computer users to take precautions beforehand in this paper a computer virus propagation model based on the kill signals called seir ks model is formulated and full dynamics of the proposed model are theoretically analyzed an epidemic threshold is obtained and the existence and uniqueness of the virus equilibrium are investigated it is proved that the virus free equilibrium and virus equilibrium are locally and globally asymptotically stable by applying routh hurwitz criterion and lyapunov functional approach the results of numerical simulations are provided that verifies the theoretical results the availability of the proposed model has been validated with following observations 1 the density of infected nodes in the proposed model drops to approximately 75 compared to the model in related literature and 2 a higher density of ks is conductive to inhibition of virus diffusion

hessian measures on the heisenberg group abstract in this paper we study the properties of k convex functions on the heisenberg group h n for 1 k 2 n and prove the weak continuity of k hessian measures with respect to local uniform convergence in the heisenberg setting our approach through monotonicity formulae makes use of previous research in the corresponding euclidean case of trudinger and wang the case k 2 n provides an analogue of the monge ampere measure of aleksandrov for h n we also answer a conjecture of garofalo and tournier on monotonicity for the cases n 2

nonatomic games on loeb spaces in the setting of noncooperative game theory strategic negligibility of individual agents or diffuseness of information has been modeled as a nonatomic measure space typically the unit interval endowed with lebesgue measure however recent work has shown that with uncountable action sets for example the unit interval there do not exist pure strategy nash equilibria in such nonatomic games in this brief announcement we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces hyperfinite loeb spaces we also emphasize other desirable properties of games on hyperfinite loeb spaces and present a synthetic treatment embracing both large games as well as those with incomplete information

the aronsson euler equation for absolutely minimizing lipschitz extensions with respect to carnot caratheodory metrics we derive the euler lagrange equation also known in this setting as the aronsson euler equation for absolute minimizers of the l variational problem formula math where c g is an open subset of a carnot group 0 u denotes the horizontal gradient of u r and the lipschitz class is defined in relation to the carnot caratheodory metric in particular we show that absolute minimizers are infinite harmonic in the viscosity sense as a corollary we obtain the uniqueness of absolute minimizers in a large class of groups this result extends previous work of jensen and of crandall evans and gariepy we also derive the aronsson euler equation for more regular absolutely minimizing lipschitz extensions corresponding to those carnot caratheodory metrics which are associated to free systems of vector fields

new properties of convex functions in the heisenberg group we prove some new properties of the weakly h convex functions recently introduced by danielli garofalo and nhieu as an interesting application of our results we prove a theorem of busemann feller alexandrov type in the heisenberg groups h n 1 2

valuations on convex sets non commutative determinants and pluripotential theory abstract a new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space h n is presented in particular new examples of sp n sp 1 invariant translation invariant continuous valuations are constructed this method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers bull sci math 127 1 2003 1 j geom anal 13 2 2003 183

the continuity and range of the quaternionic monge ampere operator on quaternionic space in this paper we use the quaternionic closed positive currents to establish some pluripotential results for quaternionic monge ampere operator by introducing a new quaternionic capacity we prove a sufficient condition which implies the weak convergence of quaternionic monge ampere measures triangle u j n rightarrow triangle u n we also obtain an equivalent condition of convergence in c n 1 capacity by using methods from xing proc am math soc 124 2 457 467 1996 as an application the range of the quaternionic monge ampere operator is discussed

on the limits of communication in multidimensional cheap talk a comment we analyze a cheap talk game a la crawford and sobel in a multidimensional state and policy space a feature of the multidimensional state space is that communication on one dimension often reveals information on others we show how this feature imposes bounds on communication

proximity of information in games with incomplete information existing notions of proximity of information fail to satisfy desired continuity properties of equilibria in games with incomplete information we demonstrate this failure and propose a topology on information structures which is the minimal one that satisfies those continuity requirements this topology is defined in terms of the common belief players have about the proximity of each player s information

lipschitz continuity aleksandrov theorem and characterizations for h convex functions in the geometries of stratified groups we show that h convex functions locally bounded from above are locally lipschitz continuous and that the class of v convex functions exactly corresponds to the class of upper semicontinuous h convex functions as a consequence v convex functions are locally lipschitz continuous in every stratified group in the class of step 2 groups we characterize locally lipschitz h convex functions as measures whose distributional horizontal hessian is positive semidefinite in euclidean space the same results were obtained by dudley and reshetnyak we prove that a continuous h convex function is a e twice differentiable whenever its second order horizontal derivatives are radon measures

isoperimetric and sobolev inequalities for carnot caratheodory spaces and the existence of minimal surfaces after hormander s fundamental paper on hypoellipticity 54 the study of partial differential equations arising from families of noncommuting vector fields has developed significantly in this paper we study some basic functional and geometric properties of general families of vector fields that include the hormander type as a special case similar to their classical counterparts such properties play an important role in the analysis of the relevant differential operators both linear and nonlinear to motivate our results we recall some classical inequalities let e c r be a caccioppoli set a measurable set having a locally finite perimeter then one has the isoperimetric inequality

the optimal dynamic immunization under a controlled heterogeneous node based sirs model abstract dynamic immunizations under which the state of the propagation network of electronic viruses can be changed by adjusting the control measures are regarded as an alternative to static immunizations this paper addresses the optimal dynamical immunization under the widely accepted sirs assumption first based on a controlled heterogeneous node based sirs model an optimal control problem capturing the optimal dynamical immunization is formulated second the existence of an optimal dynamical immunization scheme is shown and the corresponding optimality system is derived next some numerical examples are given to show that an optimal immunization strategy can be worked out by numerically solving the optimality system from which it is found that the network topology has a complex impact on the optimal immunization strategy finally the difference between a payoff and the minimum payoff is estimated in terms of the deviation of the corresponding immunization strategy from the optimal immunization strategy the proposed optimal immunization scheme is justified because it can achieve a low level of infections at a low cost

quasicontinuity and maximality of quaternionic plurisubharmonic functions abstract in this paper we establish the quaternionic versions of several results in the complex pluripotential theory by using the quaternionic closed positive currents which were introduced in 24 we show that quasicontinuity one of the most important properties of complex plurisubharmonic functions holds also for quaternionic plurisubharmonic functions in h n moreover we prove an equivalent characterization of the maximality which is central to the pluripotential theory a locally bounded plurisubharmonic function u is maximal if and only if it satisfies the homogeneous quaternionic monge ampere equation u n 0

sharp comparison and maximum principles via horizontal normal mapping in the heisenberg group in this paper we solve a problem raised by gutierrez and montanari about comparison principles for h convex functions on subdomains of heisenberg groups our approach is based on the notion of the sub riemannian horizontal normal mapping and uses degree theory for set valued maps the statement of the comparison principle combined with a harnack inequality is applied to prove the aleksandrov type maximum principle describing the correct boundary behavior of continuous h convex functions vanishing at the boundary of horizontally bounded subdomains of heisenberg groups this result answers a question by garofalo and tournier the sharpness of our results are illustrated by examples

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

h type groups and iwasawa decompositions since their introduction by a kaplan kpl some ten years ago generalised heisenberg groups also known as groups of heisenberg type or h type groups have provided a framework in which to construct interesting examples in geometry and analysis see for instance c2 kp2 kp3 kpr k2 rl r2 tl tv the iwasawa n groups associated to all the real rank one simple lie groups are h type so one has a convenient vehicle for studying these in a unified way many problems on these simple lie groups can be reduced to a problem on h type groups via the so called noncompact picture and often problems on h type groups can be solved on all the groups of the family in one fell swoop as in for example ch ck dr out of this approach to studying simple lie groups several problems arise such as why only some h type groups correspond to simple lie groups of real rank one in this paper we discuss various features of iwasawa n groups which distinguish them in the class of all h type groups we shall show that all h type groups which possess certain geometric properties clearly possessed by iwasawa n groups satisfy a lie algebraic condition implicit in the work of b kostant kt2 that we shall call the j condition we shall also use elementary clifford algebra to classify the

weak differentiability of bv functions on stratified groups we prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set we introduce functions of bounded higher order variation and obtain a weak version of alexandroff differentiability theorem in this context we present a nontrivial class of functions with second order bounded variation arising from inf convolution formula of a suitable cost function

investigation of dynamics of a virus antivirus model in complex network abstract in this paper a new model of computer virus antivirus propagation dynamics based on the topology nature of the internet is established we analyze theoretically the complex dynamics of the model and it is found that unlike the existing models the model admits two virus free equilibria and possesses possibly two virus equilibria one being antivirus independent and the other being antivirus dependent furthermore the stability of virus free equilibria is analyzed via a threshold value associated with the topology of the internet and the model parameters it is established that if the threshold value is less than or equal to the unity the virus free equilibria are alternatively globally attractive resulting in virus eradication while if the threshold value is greater than unity the antivirus independent virus equilibrium is globally asymptotically stable leading to virus diffusion while the antivirus dependent virus equilibrium also is globally asymptotically stable some numerical examples are presented to illustrate the analytical results

holder continuous solutions to quaternionic monge ampere equations abstract we prove the holder continuity of the unique solution to quaternionic monge ampere equation with densities in l p p 2 on a bounded strictly pseudoconvex domains

subharmonic functions on carnot groups many results of classical potential theory are extended to sub laplacians on carnot groups some characterizations of subharmonicity representation formulas of poisson jensen s kind and nevanlinna type theorems are proved we also characterize the riesz measure related to bounded above subharmonic functions in n

the quaternionic monge ampere operator and plurisubharmonic functions on the heisenberg group many fundamental results of pluripotential theory on the quaternionic space mathbb h n are extended to the heisenberg group we introduce notions of a plurisubharmonic function the quaternionic monge ampere operator differential operators d 0 and d 1 and a closed positive current on the heisenberg group the quaternionic monge ampere operator is the coefficient of d 0d 1u n we establish the chern levine nirenberg type estimate the existence of quaternionic monge ampere measure for a continuous quaternionic plurisubharmonic function and the minimum principle for the quaternionic monge ampere operator unlike the tangential cauchy riemann operator overline partial b on the heisenberg group which behaves badly as partial b overline partial b ne overline partial b partial b the quaternionic counterpart d 0 and d 1 satisfy d 0d 1 d 1d 0 this is the main reason that we have a good theory for the quaternionic monge ampere operator than partial b overline partial b n

on the existence of nash equilibrium in bayesian games we furnish conditions on the primitives of a bayesian game that guarantee the existence of a bayes nash equilibrium by allowing for payoff discontinuities in actions we cover various applications that cannot be handled by extant results

suboptimal solutions to team optimization problems with stochastic information structure existence uniqueness and approximations of smooth solutions to team optimization problems with stochastic information structure are investigated suboptimal strategies made up of linear combinations of basis functions containing adjustable parameters are considered estimates of their accuracies are derived by combining properties of the unknown optimal strategies with tools from nonlinear approximation theory the estimates are obtained for basis functions corresponding to sinusoids with variable frequencies and phases gaussians with variable centers and widths and sigmoidal ridge functions the theoretical results are applied to a problem of optimal production in a multidivisional firm for which numerical simulations are presented

on the existence of monotone pure strategy equilibria in bayesian games we extend and strengthen both athey s 2001 and mcadams 2003 results on the existence of monotone pure strategy equilibria in bayesian games we allow action spaces to be compact locally complete metrizable semilatttices and can handle both a weaker form of quasisupermodularity than is employed by mcadams and a weaker single crossing property than is required by both athey and mcadams our proof which is based upon contractibility rather than convexity of best reply sets demonstrates that the only role of single crossing is to help ensure the existence of monotone best replies finally we do not require the milgrom weber 1985 absolute continuity condition on the joint distribution of types

uniqueness of lipschitz extensions minimizing the sup norm of the gradient in this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values geometrically this can be interpreted as finding a minimal lipschitz extension due to the weak convexity of the functional associated to this problem solutions are generally nonunique by adopting g aronsson s notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation in fact we actually prove a weak maximum principle for this partial differential equation which in some sense is the euler equation for the minimization problem this is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity to overcome this difficulty we use the weak solutions of m g crandall and p l lions also known as viscosity solutions in conjunction with some arguments using integration by parts

generalized equilibrium results for games with incomplete information milgrom and weber milgrom p r weber r j 1985 distributional strategies for games with incomplete information math oper res 10 619 632 gave an existence result for a nash equilibrium in a game with incomplete information using their notion of a distributional strategy here we obtain a substantial improvement of their existence result in terms of the more traditional concept of a behavioral strategy this improvement is reached very naturally as an application of a theory of weak convergence for transition probabilities which is recapitulated extensively in this paper also a new result on the weak convergence of product transition probabilities is included

on the linear algebra in the quaternionic pluripotential theory abstract we clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified in particular we characterize and normalize real 2 forms with respect to the quaternionic structure and show that the moore determinant of a quaternionic hyperhermitian matrix is the coefficient of the exterior product of the associated real 2 form as a corollary the quaternionic monge ampere operator is the coefficient of the exterior product of the baston operator

uniform continuity of the value of zero sum games with differential information we establish uniform continuity of the value for zero sum games with differential information when the distance between changing information fields of each player is measured by the boylan pseudometric we also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change even with the weak topology on players strategy sets and is approximately lower semicontinuous

the aronsson equation for absolute minimizers of l infty functionals associated with vector fields satisfying hormander s condition given a carnot caratheodory metric space r d x generated by vector fields x i m i 1 satisfying hormander s condition we prove in theorem a that any absolute minimizer u w 1 x to f v q ess sup x f x xv x is a viscosity solution to the aronsson equation x i f x x u x f pi x x u x 0 in under suitable conditions on f in particular any amle is a viscosity solution to the subelliptic oo laplacian equation x u x i ux j ux i x j u 0 in if the carnot caratheodory space is a carnot group g and f is independent of the x variable we establish in theorem c the uniqueness of viscosity solutions to the aronsson equation a xu d 2 u f pi xu f pj xu x i x j u 0 in u on under suitable conditions on f as a consequence the uniqueness of both amle and viscosity solutions to the subelliptic oo laplacian equation is established on any carnot group g

a zero sum game with incomplete information and compact action spaces we make use of distributional strategies to describe player s choices of actions in a zero sum game with incomplete information and compact action spaces under very mild assumptions we obtain the existence of equilibria

viscosity solutions to quaternionic monge ampere equations abstract quaternionic monge ampere equations have recently been studied intensively using methods from pluripotential theory we present an alternative approach by using the viscosity methods we study the viscosity solutions to the dirichlet problem for quaternionic monge ampere equations d e t f f q f with boundary value f g on here is a bounded domain on the quaternionic space h n g c and f q t is a continuous function on r r which is non decreasing in the second variable we prove a viscosity comparison principle and a solvability theorem moreover the equivalence between viscosity and pluripotential solutions is shown

cheap talk and sequential equilibria in signaling games well behaved infinite signaling games may have no sequential equilibria we prove that adding cheap talk to these games solves the nonexistence problem the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap talk extension of the limit game in addition when the signaling space has no isolated points any cheap talk sequential equilibrium outcome can be approximated by a sequential e equilibrium of the game without cheap talk