universal features in the growth dynamics of complex organizations we analyze the fluctuations in the gross domestic product gdp of 152 countries for the period 1950 1992 we find that i the distribution of annual growth rates for countries of a given gdp decays with fatter tails than for a gaussian and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with results on firm growth these results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms s0031 9007 98 07339 6 pacs numbers 02 50 ey 01 75 m 05 40 j 05 45 b in the study of physical systems the analysis of the scaling properties of the fluctuations has been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior in contrast most studies on the time evolution of economic time series have concentrated on average growth rates 1 18 here we investigate the possibility that the study of fluctuations in economics may also lead to a better understanding of the mechanisms responsible for the observed dynamics 19 23 we therefore analyze the fluctuations in the growth rate of the gross domestic product gdp of 152 countries during the period 1950 1992 24 we will show that i the distribution of annual growth rates for countries of a given gdp is consistent for a certain range with an exponential decay and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with

scaling in income inequalities and its dynamical origin abstract we provide an analytically treatable model that describes in a unified manner income distribution for all income categories the approach is based on a master equation with growth and reset terms the model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the cluj county romania in agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master curve when a properly normalised income is considered the beta prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters the non universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio economic regulations

the equivalence problem of multitape finite automata abstract using a result of b h neumann we extend eilenberg s equality theorem to a general result which implies that the multiplicity equivalence problem of two nondeterministic multitape finite automata is decidable as a corollary we solve a long standing open problem in automata theory namely the equivalence problem for multitape deterministic finite automata the main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

kinematics and dynamics of pareto zipf s law and gibrat s law abstract we discuss pareto zipf s law and gibrat s law found in the high end regions of personal income company s income and various measures of company size the fact that these phenomenological laws coexist in wide range of data suggests some deep mathematical relations between them in this paper we find just such relationships under the law of detailed balance this sets a basis for perturbative treatment of the economic change

growth and fluctuations of personal income pareto s law states that the distribution of personal income obeys a power law in high income range many researchers have proposed models over a century since its discovery but the dynamical understanding of hie phenomenon necessitates empirical study on growth of individual income here we uncovered several properties in the fluctuations of individual income growth derived from income tax data including all taxpayers more than 80 000 with high income iii japan for two consecutive years 1997 and 1998 in a relatively stable period of economics in this work 8 we show i that the dynamics has approximate time reversal symmetry in the period ii that the distribution of growth rate is independent of income tax in the past yearm and iii that the pareto s law breaks down in bubble collapse of japanese economy in 1990 it is shown in 3 how these phenomenological facts are consistent with pareto law these findings provide first direct observation of dynamical process of ruuirey flow in an economic network and its relation to risky assets price fluctuations of lands and stocks

distribution of wealth in a network model of the economy abstract we show analytically and numerically that wealth distribution in the bouchaud mezard network model of the economy is described by a three parameter generalized inverse gamma distribution in the mean field limit of a network with any two agents linked it reduces to the inverse gamma distribution

shape of growth rate distribution determines the type of non gibrat s property abstract in this study the authors examine exhaustive business data on japanese firms which cover nearly all companies in the mid and large scale ranges in terms of firm size to reach several key findings on profits sales distribution and business growth trends here profits denote net profits first detailed balance is observed not only in profits data but also in sales data furthermore the growth rate distribution of sales has wider tails than the linear growth rate distribution of profits in log log scale on the one hand in the mid scale range of profits the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases this is called non gibrat s first property on the other hand in the mid scale range of sales the probability of positive growth decreases as the initial value increases while the probability of negative growth hardly changes this is called non gibrat s second property under detailed balance non gibrat s first and second properties are analytically derived from the linear and quadratic growth rate distributions in log log scale respectively in both cases the log normal distribution is inferred from non gibrat s properties and detailed balance these analytic results are verified by empirical data consequently this clarifies the notion that the difference in shapes between growth rate distributions of sales and profits is closely related to the difference between the two non gibrat s properties in the mid scale range

a pseudospectral chebychev method for the 2d wave equation with domain stretching and absorbing boundary conditions in this paper we develop a method for the simulation of wave propagation on artificially bounded domains the acoustic wave equation is solved at all points away from the boundaries by a pseudospectral chebychev method absorption at the boundaries is obtained by applying one way wave equations at the boundaries without the use of damping layers the theoretical reflection coefficient for the method is compared to theoretical estimates of reflection coefficients for a fourier model of the problem these estimates are confirmed by numerical results modification of the method by a transformation of the grid to allow for better resolution at the center of the grid reduces the maximum eigenvalues of the differential operator consequently for stability the maximum timestep iso 1 n as compared too 1 n2 for the standard chebychev method therefore the chebychev method can be implemented with efficiency comparable to that of the fourier method moreover numerical results presented demonstrate the superior performance of the new method

derivation of the distribution from extended gibrat s law abstract employing profits data of japanese companies in 2002 and 2003 we identify the non gibrat s law which holds in the middle profits region from the law of detailed balance in all regions gibrat s law in the high region and the non gibrat s law in the middle region we kinematically derive the profits distribution function in the high and middle range uniformly the distribution function accurately fits with empirical data without any fitting parameter

relations between a typical scale and averages in the breaking of fractal distribution abstract we study distributions which have both fractal and non fractal scale regions by introducing a typical scale into a scale invariant system as one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region we employ 2 dim quantum gravity modified by the r 2 term as examples of distributions in the real world which have similar property to this model we consider those of personal income in japan over latest twenty fiscal years we find relations between the typical scale and several kinds of averages in this model and observe that these relations are also valid in recent personal income distributions in japan with sufficient accuracy we show the existence of the fiscal years so called bubble term in which the gap has arisen in power law by observing that the data are away from one of these relations we confirm therefore that the distribution of this model has close similarity to those of personal income in addition we can estimate the value of pareto index and whether a big gap exists in power law by using only these relations as a result we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

poisson approach for evaluating numerical methods for the two dimensional wave equation constrained to absorbing boundary conditions abstract in order to assess the accuracy of several chebyshev pseudospectral methods proposed in the literature for solving the two dimensional wave equation we propose a numerical procedure that produces a highly accurate numerical solution based on integration of poisson s formula by gauss quadratures the motivation for this procedure is that this solution has no errors due to reflections as it happens with all numerical techniques used to solve this problem the only source of errors is the integration error which decays quickly to zero if the integrand is smooth and the number of integration points is large enough based on this solution we can evaluate easily the effects of introducing artificial boundary conditions many numerical methods depend on this approximation as a consequence of domain truncation

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

random walks with self similar clusters abstract we construct a random walk on a lattice having a hierarchy of self similar clusters built into the distribution function of allowed jumps the random walk is a discrete analog of a levy flight and coincides with the levy flight in the continum limit the fourier transform of the jump distribution function is the continuous nondifferentiable function of weierstrass we show that for cluster formation it is necessary that the mean squared displacement per jump be infinite and that the random walk be transient we interpret our random walk as having an effective dimension higher than the spatial dimension available to the walker the difference in dimensions is related to the fractal hausdorff besicovitch dimension of the self similar clusters

on the 2d bioheat equation with convective boundary conditions and its numerical realization via a highly accurate approach abstract a series solution for a 2d bioheat pennes conduction model with convective boundary conditions is established by using the classical fourier method to validate and compare results a numerical method for constructing highly accurate numerical solutions is also derived and numerically illustrated both the series solution and the proposed numerical method open interesting possibilities of application in inverse perfusion coefficient identification problems

influence of saving propensity on the power law tail of the wealth distribution some general features of statistical multi agent economic models are reviewed with particular attention to the dependence of the equilibrium wealth distribution on the agents saving propensities it is shown that in a finite system of agents with a continuous saving propensity distribution a power law tail with pareto exponent 1 can appear also when agents do not have saving propensities distributed over the whole interval between zero and one rather a power law can be observed in a finite interval of wealth whose lower and upper ends are shown to be determined by the lower and upper cutoffs respectively of the saving propensity distribution it is pointed out that a cutoff of the power law tail can arise also through a different mechanism when the number of agents is small enough numerical simulations have been carried out by implementing a procedure for assigning saving propensities homogeneously which results in a smoother wealth distributions and correspondingly wider power law intervals than other procedures based on random algorithms

a note on stability of pseudospectral methods for wave propagation in this paper we deal with the effects on stability of subtle differences in formulations of pseudospectral methods for solution of the acoustic wave equation we suppose that spatial derivatives are approximated by chebyshev pseudospectral discretizations through reformulation of the equations as first order hyperbolic systems any appropriate ordinary differential equation solver can be used to integrate in time however the resulting stability and hence efficiency properties of the numerical algorithms are drastically impacted by the manner in which the absorbing boundary conditions are incorporated specifically mathematically equivalent well posed approaches are not equivalent numerically an analysis of the spectrum of the resultant system operator predicts these properties

income distribution boltzmann analysis and its extension abstract the paper aims at describing income distribution in moderate income regions starting with dividing income behaviors into the two parts random and deterministic and by introducing instantaneous model for theoretical derivations and cumulative model for positive tests this paper applies the equilibrium approach of statistical mechanics in the study of nonconserved individual income course the random income follows a stationary distribution similar to the maxwell boltzmann distribution in the instantaneous model combining this result with marginal analysis the probability distribution of individual income process that is composed of the random and deterministic income courses approximately obeys a distribution law mixing exponential function with a logarithmic prefactor using the census or income survey data of usa uk japan and new zealand the distribution law has been tested the results show that it agrees very well with most of the empirical data the discussion suggests that there might be essentially different income processes to happen in moderate and high income regions

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

on synchronized multi tape and multi head automata motivated by applications to verification problems in string manipulating programs we look at the problem of whether the heads in a multi tape automaton are synchronized given an n tape pushdown automaton m with a one way read only head per tape and a right end marker on each tape and an integer k 0 we say that m is k synchronized if at any time during any computation of m on any input n tuple x 1 x n whether or not it is accepted no pair of input heads that are not on are more than k cells apart this requirement is automatically satisfied if one of the heads has reached note that an n tuple x 1 x n is accepted if m reaches the configuration where all n heads are on and m is in an accepting state the automaton can be deterministic dpda or nondeterministic npda and in the special case may not have a pushdown stack dfa nfa we obtain decidability and undecidability results for these devices for both one way and two way versions we also consider the notion of k synchronized one way and two way multi head automata and investigate similar problems

the scale free topology of market investments abstract we propose a network description of large market investments where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings in this framework the in degree k in and the sum of incoming link weights v of an investor correspond to the number of assets held portfolio diversification and to the invested wealth portfolio volume respectively an empirical analysis of three different real markets reveals that the distributions of both k in and v display power law tails with exponents and moreover we find that k in scales as a power law function of v with an exponent remarkably despite the values of and differ across the three markets they are always governed by the scaling relation 1 1 we show that these empirical findings can be reproduced by a recent model relating the emergence of scale free networks to an underlying paretian distribution of hidden vertex properties

a geometrical imaging of the real gap between economies of china and the united states abstract gdp of china is about 10 trillion dollars and gdp of the united states is about 18 trillion dollars suppose that we know for the coming years economy of the us will experience a real growth rate equal to 3 and economy of china will experience a real growth as of 6 now the question is how long does it take for economy of china to catch the economy of the united states the early impression is that the desired time is the answer of the equation 10 1 0 6 x 18 1 0 3 x the correct answer however is quite different gdp is not a simple number and the gap between two countries cannot be addressed simply through their sizes it is rather a geometrical object countries pass different paths in the space of production the gaps between gdp of different countries depend on the path that each country passes through and local metric to address distance between economies of china and of the us we need to know their utility preferences and the path that china passes to reach the us size the true gap then can be found if we calculate local metric along this path it resembles impressions about measurements in the general theory of relativity path dependency of measurements is an old known fact in economy it is widely discussed in the index number theory our aim is to stick to the geometrical view presented in the general relativity to provide a fast impression about the matter for physicists we show that different elements in the general relativity have their own counterparts in economics we claim that national agencies who provide aggregate data resemble falling observers into a curved space time it is while the world bank or international organizations are outside observers

heavy tailed targets and ab normal asymptotics in diffusive motion abstract we show that under suitable confinement conditions the ordinary fokker planck equation may generate non gaussian heavy tailed probability density functions pdfs like for example cauchy or more general levy stable distributions in its long time asymptotics in fact all heavy tailed pdfs known in the literature can be obtained this way for the underlying diffusion type processes our main focus is on their transient regimes and specifically the crossover features when an initially infinite number of pdf moments decreases to a few or none at all the time dependence of the variance if in existence t with 0 2 may in principle be interpreted as a signature of subdiffusive normal diffusive or superdiffusive behavior under confining conditions the exponent is generically well defined in substantial periods of time however there is no indication of any universal time rate hierarchy due to a proper choice of the driver and or external potential

the uniqueness of firm size distribution function from tent shaped growth rate distribution abstract employing profits data of japanese firms in 2003 and 2004 we report the proof that a non gibrat s law in the middle scale region of profits is unique under the law of detailed balance this uniquely leads to the probability distribution function pdf of profits in the proof two approximations are employed the pdf of growth rate is described as tent shaped exponential functions and the value of the origin of the growth rate distribution is constant these approximations are confirmed in the database the resultant profits pdf fits with the empirical data consistently this guarantees the validity of the approximations

entropic basis of the pareto law based on the assumption that certain economies achieve quasi equilibrium an appropriate economic statistical thermodynamics is formulated in which entropy emerges naturally under the assumption that the small group of high income agents whose income distribution satisfies pareto s law does not much interact with the larger group of lower income agents the corresponding statistical thermodynamic relations are applied in order to derive the pareto law the derivation requires the assumption that the sum of logarithms of the incomes of the individual agents or the product of incomes in this group is conserved a strong plausibility argument for this assumption is presented it also turns out in accordance with intuition that in order to increase the average income of an agent more risk in the form of greater entropy production must be assumed other consequences are discussed and an experimental demonstration of the uniformity of economic temperature in a system at economic equilibrium is presented

absorbing boundary conditions for diffusion equations summary we construct and analyse a family of absorbing boundary conditions for diffusion equations with variable coefficients curved artifical boundary and arbitrary convection it relies on the geometric identification of the dirichlet to neumann map and rational interpolation of z 1 2 in the complex plane the boundary conditions are stable accurate and practical for computations

the growth of business firms theoretical framework and empirical evidence we introduce a model of proportional growth to explain the distribution pg g of business firm growth rates the model predicts that pg g is exponential in the central part and depicts an asymptotic power law behavior in the tails with an exponent 3 because of data limitations previous studies in this field have been focusing exclusively on the laplace shape of the body of the distribution in this article we test the model at different levels of aggregation in the economy from products to firms to countries and we find that the predictions of the model agree with empirical growth distributions and size variance relationships

the emergence of different tail exponents in the distributions of firm size variables abstract we discuss a mechanism through which inversion symmetry i e invariance of a joint probability density function under the exchange of variables and gibrat s law generate power law distributions with different tail exponents using a dataset of firm size variables that is tangible fixed assets k the number of workers l and sales y we confirm that these variables have power law tails with different exponents and that inversion symmetry and gibrat s law hold based on these findings we argue that there exists a plane in the three dimensional space log k log l log y with respect to which the joint probability density function for the three variables is invariant under the exchange of variables we provide empirical evidence suggesting that this plane fits the data well and argue that the plane can be interpreted as the cobb douglas production function which has been extensively used in various areas of economics since it was first introduced almost a century ago

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

distribution of individual incomes in china between 1992 and 2009 abstract this paper presents comprehensive analysis of the evolution of the distribution of individual annual incomes across the majority of the population in china from 1992 2009 the cumulative distribution functions cdfs and probability density functions pdfs are presented overall the cdfs follow the gaussian function c x a e x 2 2 2 for the majority of individuals in the population while the pdfs obey the function p x b x e x 2 2 2 the width of the pdf has widened from 1992 to 2009 suggesting the factor x has been progressively skewing the curve to the right this long tail representing the high income range is reminiscent of an exponential distribution curve this indicates that a few individuals obtain extremely high incomes leading to increasing levels of financial inequality in china

a family network model for wealth distribution in societies a model based on first degree family relations network is used to describe the wealth distribution in societies the network structure is not a priori introduced in the model it is generated in parallel with the wealth values through simple and realistic dynamical rules the model has two main parameters governing the wealth exchange in the network choosing their values realistically leads to wealth distributions in good agreement with measured data the cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit and shows the pareto like power law tail for the upper 5 of the society the obtained pareto indexes are in good agreement with the measured ones the generated family networks also converge to a statistically stable topology with a simple poissonian degree distribution on this family network many interesting correlations are studied and the main factors leading to wealth diversification and the formation of the pareto law are identified

stability of a chebychev pseudospectral solution of the wave equation with absorbing boundaries abstract stability of the pseudospectral chebychev collocation solution of the two dimensional acoustic wave problem with absorbing boundary conditions is investigated the continuous one dimensional problem with one absorbing boundary and one dirichlet boundary has previously been shown to be far from normal consequently the spectrum of that problem says little about the stability behavior of the solution our analysis proves that the discrete formulation with dirichlet boundaries at all boundaries is near normal and hence the formulation with absorbing boundaries at all boundaries either for one dimensional or two dimensional wave propagation is not far from normal the near normality follows from the near normality of the second order derivative pseudospectral differential operator further the nearness to normality is independent of the boundary discretization stability limits on the timestep are however dependent on the boundary operator with an explicit euler method having the most restrictive condition the crank nicolson implementation has a stability limit the same as the dirichlet formulation furthermore in this case the restriction scales by 1 2 in moving from one dimension to two dimensions exactly as in the central finite difference approximation numerical results confirm the predicted values on allowable timesteps obtained from a spectral analysis for both chebychev and modified chebychev implementations we conclude that the spectrum of the evolution operator is informative for predicting the behavior of the numerical solution

new decidability results concerning two way counter machines the authors study some decision questions concerning two way counter machines and obtain the strongest decidable results to date concerning these machines in particular it is shown that the emptiness containment and equivalence ece for short problems are decidable for two way counter machines whose counter is reversal bounded i e the counter alternates between increasing and decreasing modes at most a fixed number of times this result is used to give a simpler proof of a recent result in which the ece problems for two way reversal bounded pushdown automata accepting bounded languages i e subsets of w 1 ldots w k for some nonnull words w 1 ldots w k are decidable other applications concern decision questions about simple programs finally it is shown that nondeterministic two way reversal bounded multicounter machines are effectively equivalent to finite automata on unary languages and hence their ece problems are decidable also

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

a trade investment model for distribution of wealth econophysics provides a strategy for understanding the potential mechanisms underlying the anomalous distribution of wealth found in real societies we present a computational nonlinear stochastic model for the distribution of wealth that depends upon three parameters and two mechanisms trade and investment to avoid economic paradoxes the trade mechanism is assumed to be related to the poorer trader s wealth and to statistically advantage the poorer of the two traders the two mechanisms together are shown to generate a distribution that reproduces the full range of the empirical wealth distribution and not only the inverse power law tail that pareto found in western societies at the end of the 19th century

on the irreconcilability of pareto and gibrat laws abstract if business firms face a multiplicative growth process in which their growth rates are laplace distributed and independent from their sizes the size cannot be distributed according to a stationary pareto distribution recent contributions using formal arguments seem to contrast with these statements we prove that the proposed formal results are wrong

properties of wealth distribution in multi agent systems of a complex network abstract we present a simple model for examining the wealth distribution with agents playing evolutionary games the prisoners dilemma and the snowdrift game on complex networks pareto s power law distribution of wealth from 1897 is reproduced on a scale free network and the gibbs or log normal distribution for a low income population is reproduced on a random graph the pareto exponents of a scale free network are in agreement with empirical observations the gini coefficient of an er random graph shows a sudden increment with game parameters we suggest that the social network of a high income group is scale free whereas it is more like a random graph for a low income group

annual change of pareto index dynamically deduced from the law of detailed quasi balance abstract employing data on the assessed value of land in 1983 2005 japan we investigate the dynamical behavior in the high scale region of non equilibrium systems from the detailed quasi balance and gibrat s law we derive a relation between the change of pareto index and a symmetry in the detailed quasi balance the relation is confirmed in the empirical data nicely