conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

a renormalisation group analysis of the semi finite potts model we discuss the ordinary transition of the semi infinite q state potts model within the migdal kadanoff renormalisation group scheme approximate surface free energies are calculated in dimension d 2 in addition we consider the effect of symmetry breaking surface fields our scheme predicts that only one such field is relevant

further results on the asymptotic agreement problem the problem of reaching a concensus between two decision makers provided with different information is considered the problem in which the decision makers may have different underlying probability models is studied results are developed to characterize the likelihood of an agreement being reached eventually in terms of the nature of the inter decision maker communications the problem in which the decision makers are aware of the possibility that they may have different models is treated it is found that in this case a deadlock can be reached where neither decision maker can learn additional information from the concensus process and they cannot reach a concensus decision this result indicates that incorporating human uncertainty in probability assessment into the asymptotic agreement problem can lead to outcomes not anticipated in the general theory previously developed

some results concerning the generic continuity of set valued mappings abstract a theorem proved by fort in 1951 states that an upper semi continuous mapping from a baire space x into non empty compact subsets of a metric space is both lower and upper semi continuous at the points of a dense residual set of x in this paper we present several results concerning the generic continuity of set valued mappings first we demonstrate that generic continuity in the sense of baire category cannot be extended to almost everywhere continuity with respect to some measure then we show that baireness of the domain space is a necessary condition for fort s theorem to hold finally we show that fort s theorem holds without any compactness assumption on the images of the set valued mapping

mechanism design with collusion and correlation in a public good environment with positively correlated types we characterize optimal mechanisms when agents have private information and can enter collusive agreements first we prove a weak collusion proof principle according to which there is no restriction for the principal in offering weak collusion proof mechanisms second with this principle we characterize the set of allocations that satisfy individual and coalitional incentive constraints the optimal weakly collusion proof mechanism calls for distortions away from first best efficiency obtained without collusion allowing collusion restores continuity between the correlated and the uncorrelated environments when the correlation becomes almost perfect first best efficiency is approached finally the optimal collusion proof mechanism is strongly ratifiable

discounted robust stochastic games and an application to queueing control this paper presents a robust optimization model for n person finite state action stochastic games with incomplete information we consider nonzero sum discounted stochastic games in which none of the players knows the true data of a game and each player adopts a robust optimization approach to address the uncertainty we call these games discounted robust stochastic games such games allow us to use simple uncertainty sets for the unknown data and eliminate the need to have an a priori probability distribution over a set of games we prove the existence of equilibrium points and propose an explicit mathematical programming formulation for an equilibrium calculation we illustrate the use of discounted robust stochastic games in a single server queueing control problem

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

bounds for best response functions in binary games abstract this paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs the best response function gives the utility maximizing response to a decision of the other players this is analogous to the response function in the treatment response literature taking the decision of the other players as the treatment except that the best response function has additional structure implied by the associated utility maximization problem further the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment response literature we focus especially on the case of a complete information entry game with two firms we also discuss the case of an entry game with many firms non entry games and incomplete information our analysis of the entry game is based on the observation of realized entry decisions which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms including the assumption of nash equilibrium play the symmetry of the payoffs between firms and whether mixed strategies are admitted

rationalizability and correlated equilibria we discuss the unity between the two standard approaches to noncooperative solution concepts for games the decision theoretic approach starts from the assumption that the rationality of the players is common knowledge this leads to the notion of correlated rationalizability it is shown that correlated rationalizability is equivalent to a posteriori equilibrium a refinement of subjective correlated equilibrium hence a decision theoretic justification for the equilibrium approach to game theory is provided an analogous equivalence result is proved between independent rationalizability which is the appropriate concept if each player believes that the others act independently and conditionally independent a posteriori equilibrium a characterization of nash equilibrium is also provided

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

strongly essential set of ky fan s points and the stability of nash equilibrium abstract in this paper a stronger perturbation of inequality functions and set valued mappings is proposed by means of the hausdorff upper semi metric which includes the perturbations defined by sup norm of function and the maximum hausdorff metric of section mapping based on this perturbation a class of strongly essential sets of ky fan s points is introduced and the existence of the strongly essential component of ky fan s points is proved as an application we use the equivalence of nash equilibrium with ky fan s points to obtain the existence of the strongly essential component of equilibrium which not only give a class of stronger essential sets but also provide a method to discuss the stability with respect to the perturbation of strategic sets

distributed algorithms for the computation of noncooperative equilibria abstract in this paper a general class of nonquadratic convex nash games is studied from the points of view of existence stability and iterative computation of noncooperative equilibria conditions for contraction of general nonlinear operators are obtained which are then used in the stability study of such games these lead to existence and uniqueness conditions for stable nash equilibrium solutions under both global and local analysis also convergence of an algorithm which employs inaccurate search techniques is verified it is shown in the context of a fish war example that the algorithm given is in some aspects superior to various algorithms found in the literature and is furthermore more meaningful for real world implementation

the spectra of quantum chains with free boundary conditions and virasoro algebras at the critical point the spectra of quantum chains with periodic and twisted boundary conditions are described by irreducible representations of two virasoro algebras with the same central charge the authors show that in the case of free boundary conditions the spectra can be understood in terms of irreducible representations of a single virasoro algebra for the ising and the three state potts models the corresponding irreducible representations are identified

surface order parameter in three dimensional percolation the authors calculate numerically by a transfer matrix algorithm the critical exponent of the surface order parameter s for the case of the ordinary transition their result s 0 98 0 02 agrees with recently published series expansion results s 1 04 0 05 and e expansion results with pade approximants s 1 01 0 06

logarithmic corrections for the percolative properties of the four state potts model clusters in the potts model are connected sets of nearest neighbour sites for which the spin variables are in the same state droplets can be obtained by adding bonds with probability p 1 exp k between the sites in a cluster where k is the potts model s inverse temperature when q to 4 renormalization group rg fixed points describing clusters and droplets will coalesce leading to logarithmic corrections we calculate the precise form of these corrections used in a differential rg method our predictions are then tested using extensive monte carlo calculations theory and the simulations are found to be in excellent agreement

entropy flux splittings for hyperbolic conservation laws part i general framework a general framework is proposed for the derivation and analysis of flux splittings and the corresponding flux splitting schemes for systems of conservation laws endowed with a strictly convex entropy the approach leads to several new properties of the existing flux splittings and to a method for the construction of entropy flux splittings for general situations a large family of genuine entropy flux splittings is derived for several significant examples the scalar conservation laws the p system and the euler system of isentropic gas dynamics in particular for the isentropic euler system we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy for this system it is proved that there exists a unique genuine entropy flux splitting that satisfies all of the entropy inequalities which is also the unique diagonalizable splitting this splitting can be also derived by the so called kinetic formulation simple and useful difference schemes are derived from the flux splittings for hyperbolic systems such entropy flux splitting schemes are shown to satisfy a discrete cell entropy inequality for the diagonalizable splitting schemes an a priori l estimate is provided by applying the principle of bounded invariant regions the convergence of entropy flux splitting schemes is proved for the 2 2 systems of conservation laws and the isentropic euler system 1995 john wiley sons inc

virtual implementation in iteratively undominated strategies complete information we investigate the implementation of social choice functions in complete information environments we consider social choice functions scf s which map from a finite set of preference profiles to lotteries over alternatives and require virtual implementation in iteratively undominated strategies an scf x is virtually implementable in iteratively undominated strategies if for all e 0 there exists an scf y which is e close to x that is for all preference profiles x and y map to lotteries which are within e of one another and which is exactly implementable in iteratively undominated strategies under very weak domain restrictions we show that if there are three or more players any scf is virtually implementable in iteratively undominated strategies a noteworthy feature of our constructions is that we only employ finite mechanisms as a corollary we obtain virtual implementation in pure and mixed strategy nash equilibrium using well behaved in particular finite mechanisms the literature on implementation in nash equilibrium and its refinements is compromised by its reliance on game forms with unnatural features for example integer games or modulo constructions with mixed strategies arbitrarily excluded in contrast our results allow for mixed strategies and do not rely on mechanisms with obviously suspicious features

optimal auction design this paper considers the problem faced by a seller who has a single object to sell to one of several possible buyers when the seller has imperfect information about how much the buyers might be willing to pay for the object the seller s problem is to design an auction game which has a nash equilibrium giving him the highest possible expected utility optimal auctions are derived in this paper for a wide class of auction design problems

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

conformal invariance finite size scaling and surface magnetic exponent of the potts model in two dimensions the analysis of renormalisation group equations for the q state potts model in two dimensions is generalised to include the presence of a surface field hs besides the bulk one hb combined with conformal invariance results this allows prediction of a surface susceptibility behaviour delta 2 f delta hs delta hb approximately l 1 8 1 c lnl 15 16 for a q 4 system of size l at the critical temperature this prediction is checked by a monte carlo based finite size scaling analysis which also nicely reproduces the exact and conjectured magnetic surface exponents for q 2 and 3 respectively for the baxter wu model similar methods give results consistent with the q 4 behaviour without logarithmic corrections c 0

existence uniqueness and computation of robust nash equilibria in a class of multi leader follower games the multi leader follower game can be looked on as a generalization of the nash equilibrium problem which contains several leaders and followers recently the multi leader follower game has been drawing more and more attention for example in power markets on the other hand in such real world problems uncertainty normally exists and sometimes cannot simply be ignored to handle mathematical programming problems with uncertainty the robust optimization technique assumes that the uncertain data belong to some sets and the objective function is minimized with respect to the worst case scenario in this paper we focus on a class of multi leader single follower games under uncertainty with some special structure we particularly assume that the follower s problem contains only equality constraints by means of the robust optimization technique we first formulate the game as the robust nash equilibrium problem and then as the generalized variational inequality gvi problem we then establish some res

evolution of players misperceptions in hypergames under perfect observations this paper considers games of incomplete information and studies the evolution of the not necessarily consistent perceptions of the players using the framework of hypergames the focus is on developing methods to modify the players perception about other players preferences by incorporating the lessons learned from observing their actions if players are rational our first update mechanism called swap learning is guaranteed to decrease the mismatch between a player s perception and the true payoff structure of other players however this method can lead to inconsistencies in the stability properties of the resulting perception this motivates the introduction of a second update mechanism called modified swap learning that is guaranteed to produce a consistent perception we also identify a class of hypergames for which modified swap is also guaranteed to decrease the mismatch in a player s perception we introduce the novel notion of h digraph as a useful tool to encode the information in a hypergame and fully characterize how this digraph is affected by changes in the players beliefs

multiple goal non cooperative conflicts under uncertainty a fuzzy set approach abstract this paper investigates strategy selection for a participant in a two party non cooperative conflict which involves both uncertainty and multiple goals uncertainty arises from the players not knowing the utility functions multiple objectives appear as the result of the payoff being a vector of prizes and the players attempt to attain various goals for each prize separately the main objective is to present a fuzzy set fuzzy programming solution concept to the conflict situation in doing so we compare a bayesian player to one that employs fuzzy set techniques we point out some of the advantages of the fuzzy set method the necessary computations in the fuzzy set method are explained in detail through an 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

causal discourse in a game of incomplete information notions of cause and effect are fundamental to economic explanation although concepts such as price effects are intuitive rigorous foundations justifying causal discourse in the wide range of economic settings remain lacking we illustrate this deficiency using an n bidder private value auction posing causal questions that cannot be addressed within existing frameworks we extend the frameworks of pearl 2000 and white and chalak 2009 to introduce topological settable systems tss a causal framework capable of delivering the missing answers particularly tss accommodate choices belonging to general function spaces our analysis suggests how tss enable causal discourse in various areas of economics

learning algorithms for two person zero sum stochastic games with incomplete information this paper investigates conditions under which two learning algorithms playing a zero sum sequential stochastic game would arrive at optimal pure strategies neither player has knowledge of either the pay off matrix or the choice of strategies available to the other and both players update their own strategies at every stage entirely on the basis of the random outcome at that stage the proposed learning algorithms are shown to converge to the optimal pure strategies when they exist with probabilities as close to 1 as desired

strategic power allocation with incomplete information in the presence of a jammer in this paper distributed competitive interactions between a secondary user su transmitter receiver pair and a jammer are investigated using a game theoretic framework under physical interference restrictions power budget constraints and incomplete knowledge of channel gains in this game the su transmitter is expected to choose its power strategy with the objective of satisfying a minimum signal to interference plus noise ratio sinr at the corresponding receiver similarly the jammer s objective is to strategically allocate its power so that the sinr constraint of the su is not satisfied due to a lack of complete information this strategic power allocation problem between the two players is modeled as a bayesian game for which the self enforcing strategies of the su transmitter receiver pair and the jammer are analyzed furthermore probability distributions are employed by the corresponding players to model the incomplete nature of the game the solution of the game corresponds to nash equilibria points equilibrium analysis is carried out by considering the mixed strategy solution space and numerical examples are presented for illustration

an equilibrium theory for multiperson decision making with multiple probabilistic models this paper develops an equilibrium theory for two person two criteria stochastic decision problems with static information patterns wherein the decision makers dm s have different probabilistic models of the underlying process the objective functionals are quadratic and the decision spaces are general inner product spaces under two different modes of decision making viz symmetric and asymmetric sufficient conditions are obtained for the existence and uniqueness of equilibrium solutions stable in the former case and in each case a uniformly convergent iterative scheme is developed whereby the equilibrium policies of the dm s can be obtained by evaluating a number of conditional expectations when the probability measures are gaussian the equilibrium solution is linear under the symmetric mode of decision making whereas it is generically nonlinear in the asymmetric case with the linear structure prevailing only in some special cases which are delineated in the paper

semiparametric identification of binary decision games of incomplete information with correlated private signals abstract this paper studies the identification and estimation of a static binary decision game of incomplete information we make no parametric assumptions on the joint distribution of private signals and allow them to be correlated we show that the parameters of interest can be point identified subject to a scale normalization under mild support requirements for the regressors publicly observed state variables and errors private signals following manski and tamer 2002 we propose a maximum score type estimator for the structural parameters and establish the asymptotic properties of the estimator

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

comment subjective probability and the theory of games comments on kadane and larkey s paper the normative solution concepts of game theory try to provide a clear mathematical characterization of what it means to act rationally in a game where all players expect each other to act rationally kadane and larkey reject the use of these normative solution concepts yet this amounts to throwing away an important piece of information to the effect that the players are rational and expect each other to be rational even in situations where the players do not expect each other to act with complete rationality normative game theory can help them heuristically to formulate reasonable expectations about the other players behavior

beliefs about beliefs without probabilities this paper constructs a space of states of the world representing the exhaustive uncertainty facing each player in a strategic situation the innovation is that preferences are restricted primarily by regularity conditions and need not conform with subjective expected utility theory the construction employs a hierarchy of preferences rather than of beliefs as in the standard bayesian model the framework is sufficiently general to accommodate uncertainty averse preferences such as exhibited in the ellsberg paradox and to allow common knowledge of expected utility or choquet expected utility to be well defined formally applications include the provision of i foundations for a harsanyi style game of incomplete information and ii a rich framework for the axiomatization of solution concepts for complete information normal form games

deriving and analysing optimal strategies in bayesian models of games wilson 1986 gives a backwards induction algorithm for sequentially obtaining the optimal next move in a repeated bayesian game in this paper we show how to identify the form of an optimal solution of such a game by a graphical procedure by means of the prisoner s dilemma game we illustrate how wilson s algorithm can be enhanced using the derived analytic form of the solution to produce an explicit optimal strategy we can then determine not only how p1 should play on all subsequent moves of the game but also use ideas of bayes rationality to discuss whether a given model of p2 s reactions is realistic

on the generic im possibility of full surplus extraction in mechanism design a number of studies most notably cremer and mclean 1985 1988 have shown that in harsanyi type spaces of a fixed finite size it is generically possible to design mechanisms that extract all the surplus from players and as a consequence implement any outcome as if the players private information were commonly known in contrast we show that within the set of common priors on the universal type space the subset of priors that permit the extraction of the players full surplus is shy shyness is an otion of smallness for convex subsets of infinite dimensional topological vector spaces in our case the set of common priors which generalizes the usual notion of zero lebesgue measure in finite dimensional spaces

surface fractal dimension of two dimensional percolation the author determines the surface fractal dimension ds for two dimensional percolation from monte carlo data in finite systems the results agree with the prediction from conformal invariance ds 2 3

epistemic conditions for nash equilibrium game theoretic reasoning has been widely applied in economics in recent years undoubtedly the most commonly used tool has been the strategic equilibrium of nash ann math 54 286 295 1951 or one or another of its so called refinements though much effort has gone into developing these refinements relatively little attention has been paid to a more basic question why consider nash equilibrium in the first place

games with incomplete information played by bayesian players i iii this article originally appeared in management science november 1967 volume 14 number 3 pp 159 182 published by the institute of management sciences the paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation such as the payoff functions the strategies available to various players the information other players have about the game etc however each player has a subjective probability distribution over the alternative possibilities in most of the paper it is assumed that these probability distributions entertained by the different players are mutually consistent in the sense that they can be regarded as conditional probability distributions derived from a certain basic probability distribution over the parameters unknown to the various players but later the theory is extended also to cases where the different players subjective probability distributions fail to satisfy this consistency assumption in cases where the consistency assumption holds the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution and the outcome of this lottery will decide which particular subgame will be played i e what the actual values of the relevant parameters will be in the game yet each player will receive only partial information about the outcome of the lottery and about the values of these parameters however every player will know the basic probability distribution governing the lottery thus technically the resulting game will be a game with complete information it is called the bayes equivalent of the original game part i of the paper describes the basic model and discusses various intuitive interpretations for the latter part ii shows that the nash equilibrium points of the bayes equivalent game yield bayesian equilibrium points for the original game finally part iii considers the main properties of the basic probability distribution

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

new developments in kinetic schemes kinetic schemes for the numerical solution of pde of fluid dynamics are a new class of upwind schemes the moment method strategy used in constructing these schemes is based on the connection between the boltzmann equation of kinetic theory of gases and governing equations of fluid dynamics any upwind scheme for the solution of the boltzmann equation becomes an upwind scheme for the solution of pde of fluid dynamics by taking suitable moments this idea has been exploited in the present paper in developing least squares kinetic upwind method lskum and kinetic flux vector splitting method on moving grid kfmg the robustness and versatility of lskum has been demonstrated by applying it to 2 d flow problems of inviscid gas dynamics the lskum has been found to operate on any type of grid and can be called a grid fault tolerant scheme in view of the use of least squares approximation to the space derivatives the kfmg is a promising new method showing how easily the kinetic schemes lend themselves easily to problems involving moving grids which are generally employed while solving problems in unsteady aerodynamics

a structure theorem for rationalizability with application to robust predictions of refinements rationalizability is a central solution concept of game theory economic models often have many rationalizable outcomes motivating economists to use refinements of rationalizability including equilibrium refinements in this paper we try to achieve a general understanding of when this multiplicity occurs and how one should deal with it assuming that the set of possible payoff functions and belief structures is sufficiently rich we establish a revealing structure of the correspondence of beliefs to sets of rationalizable outcomes we show that for any rationalizable action a of any type we can perturb the beliefs of the type in such a way that a is uniquely rationalizable for the new type this unique outcome will be robust to further small changes when multiplicity occurs then we are in a knife edge case where the unique rationalizable outcome changes sandwiched between open sets of types where each of the rationalizable actions is uniquely rationalizable as an immediate application of this result we characterize for any refinement of rationalizability the predictions that are robust to small misspecifications of interim beliefs these are only those predictions that are true for all rationalizable strategies that is the predictions that could have been made without the refinement

theory of boundary effects in invasion percolation we study the boundary effects in invasion percolation ip with and without trapping we find that the presence of boundaries introduces a new set of surface critical exponents as in the case of standard percolation numerical simulations show a fractal dimension for the region of the percolating cluster near the boundary remarkably different from the bulk one in fact on the surface we find a value of for ip with trapping compared with the bulk value of we find a logarithmic crossover from surface to bulk fractal properties as one would expect from the finite size theory of critical systems the distribution of the quenched variables on the growing interface near the boundary self organizes into an asymptotic shape characterized by a discontinuity at a value which coincides with the bulk critical threshold the exponent of the boundary avalanche distribution for ip without trapping is this value is very near to the bulk one then we conclude that only the geometrical properties fractal dimension of the model are affected by the presence of a boundary while other statistical and dynamical properties are unchanged furthermore we are able to present a theoretical computation of the relevant critical exponents near the boundary this analysis combines two recently introduced theoretical tools the fixed scale transformation and the run time statistics which are particularly suited for the study of irreversible self organized growth models with quenched disorder our theoretical results are in rather good agreement with numerical data

extensive form correlated equilibrium definition and computational complexity this paper defines the extensive form correlated equilibrium efce for extensive games with perfect recall the efce concept extends aumann s strategic form correlated equilibrium ce before the game starts a correlation device generates a move for each information set this move is recommended to the player only when the player reaches the information set in two player perfect recall extensive games without chance moves the set of efce can be described by a polynomial number of consistency and incentive constraints assuming p is not equal to np this is not possible for the set of ce or if the game has chance moves

finitely additive beliefs and universal type spaces in this paper we examine the existence of a universal to be precise terminal type space when beliefs are described by finitely additive probability measures we find that in the category of all type spaces that satisfy certain measurability conditions measurability for some fixed regular cardinal there is a universal type space i e a terminal object that is a type space to which every type space can be mapped in a unique beliefs preserving way the morphisms of our category the so called type morphisms while by an probabilistic adaption of the elegant sober drunk example of heifetz and samet 1998a we show that if all subsets of the spaces are required to be measurable there is no universal type space

bulk surface and hull fractal dimension of critical ising clusters in d 2 the authors present accurate numerical calculations of the fractal dimension d and surface dimension ds of the critical ising cluster in d 2 the results clearly support the values d 187 96 ds 5 6 which are consistent with ising clusters being described by tricritical q 1 potts model exponents from this the hull dimension dh of critical ising clusters is found to be dh 11 8 consistent with numerical work of other authors

subjective probability and the theory of games this paper explores some of the consequences of adopting a modern subjective view of probability for game theory the consequences are substantial the subjective view of probability clarifies the important distinction between normative and positive theorizing about behavior in games a distinction that is often lost in the search for solution concepts which largely characterizes game theory since the work of von neumann and morgenstern many of the distinctions that appear important in conventional game theory two person versus n person zero sum versus variable sum appear unimportant in the subjective formulation other distinctions such as single play versus repetitive play games appear to be more important in the subjective formulation than in the conventional formulation

non zero sum two person repeated games with incomplete information characterization of all equilibria of nonzero sum two person repeated games with incomplete information in the standard one sided information case informally each such equilibrium is described by a sequence of communications between the players consisting of information transmission and coordination leading to some individually rational agreement formally the concept of a bi martingale is introduced

high order positivity preserving kinetic schemes for the compressible euler equations we present a new class of high order kinetic flux splitting schemes for the compressible euler equations and we prove that these schemes are positivity preserving i e rho and t remain geq 0 the first order kinetic scheme is based on the maxwellian equilibrium function and was initially proposed by pullin j comput phys 34 1980 pp 231 244 our higher order extension can be seen as a variant of the corrected antidiffusive flux approach the necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity

conformal invariance and surface critical behaviour of a quantum chain with three spin interaction an ising model with three spin interaction is investigated by finite size scaling applying free boundary conditions the surface critical properties of the model were determined by conformal invariance taking into account logarithmic corrections the surface critical exponents obtained are in accordance with the four state potts values

steady state learning and nash equilibrium we study the steady states of a system in which players learn about the strategies their opponents are playing by updating their bayesian priors in light of their observations players are matched at random to play a fixed extensive form game and each player observes the realized actions in his own matches but not the intended off path play of his opponents or the realized actions in other matches because players are assumed to live finite lives there are steady states in which learning continually takes place if lifetimes are long and players are very patient the steady state distribution of actions approximates that of a nash equilibrium

approximate equilibria for bayesian games in this paper the problem of the existence of approximate equilibria in mixed strategies is central sufficient conditions are given under which approximate equilibria exist for non finite bayesian games further one possible approach is suggested to the problem of the existence of approximate equilibria for the class of multicriteria bayesian games

final coalgebras for functors on measurable spaces we prove that every functor on the category meas of measurable spaces built from the identity and constant functors using products coproducts and the probability measure functor d has a final coalgebra our work builds on the construction of the universal harsanyi type spaces by heifetz and samet and papers by rosziger and jacobs on coalgebraic modal logic we construct logical languages probabilistic logics of transition systems and interpret them on coalgebras the final coalgebra is carried by the set of descriptions of all points in all coalgebras for the category set we work with the functor d of discrete probability measures we prove that every functor on set built from d and the expected functors has a final coalgebra the work for set differs from the work for meas negation in needed for final coalgebras on set but not for meas

stable equilibria a reformulation part i definition and basic properties a reformulation of stable equilibria is given yielding a number of additional properties like backwards induction while still giving typically i e except in made up examples the same solutions

reputation and commitment in two person repeated games without discounting two person repeated games with no discounting are considered where there is uncertainty about the type of the players if there is a possibility that a player is an automaton committed to a particular pure or mixed stage game action then this provides a lower bound on the nash equilibrium payoffs to a normal type of this player the lower bound is the best available and is robust to the existence of other types the results are extended to the case of two sided uncertainty this work extends schmidt 1993 who analysed the restricted class of conflicting interest games

kinetic symmetrizations and pressure laws for the euler equations abstract the symmetrizations of the compressible euler equations written as kinetic mean are studied some of their properties are pointed out we emphasize for numerical purpose the case of real rarefied gases with pressure laws p f flux splitting formulae are derived for such pressure laws

one sided adaptation for infinite horizon linear quadratic n person non zero sum dynamic games and sensitivity analysis in this paper we consider a class of infinite horizon discrete time linear quadratic n person games in which one of the players lacks complete information about the game with the assumptions of a perfect state information pattern and steady state feedback strategies we convert the original game problem into a multivariable adaptive control problem by making use of the concept of fictitious play and the scheme of adaptive control for the proposed adjustment procedure we prove that each element of the estimates converges to its corresponding true value under the condition of persistent excitation we also carry out a sensitivity analysis of performance indices with respect to the embedded unknowns by using multiple models