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Register a new userModeling wealth distribution in growing markets
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We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agent could also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.
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The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we show that, depending on the values of their parameters, they can be used to generate all the relevant distributions. We also show numerically that in order to generate the power-law tail an heterogeneous risk aversion model is required. By changing the parameters of these operators one can also fine tune the resulting distributions in order to provide support for the emergence of a more egalitarian wealth distribution.
This paper analyzes the equilibrium distribution of wealth in an economy where firms productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistributes the collected resources to dynasties. The equilibrium distribution of wealth is explicitly calculated and its shape crucially depends on market incompleteness. In particular, a Paretian law in the top tail only arises if capital markets are incomplete. The Pareto exponent depends on the saving rate, on the net return on capital, on the growth rate of population and on portfolio diversification. On the contrary, the characteristics of the labour market mostly affects the bottom tail of the distribution of wealth. The analysis also suggests a positive relationship between growth and wealth inequality.
We propose an extended public goods interaction model to study the evolution of cooperation in heterogeneous population. The investors are arranged on the well known scale-free type network, the Barab{a}si-Albert model. Each investor is supposed to preferentially distribute capital to pools in its portfolio based on the knowledge of pool sizes. The extent that investors prefer larger pools is determined by investment strategy denoted by a tunable parameter $alpha$, with larger $alpha$ corresponding to more preference to larger pools. As comparison, we also study this interaction model on square lattice, and find that the heterogeneity contacts favors cooperation. Additionally, the influence of local topology to the game dynamics under different $alpha$ strategies are discussed. It is found that the system with smaller $alpha$ strategy can perform comparatively better than the larger $alpha$ ones.
In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. It is of great importance to understand the underlying mechanisms of the occurrence of such differences. By incorporating pair pattern strategies and reference point strategies into an agent-based model, we have investigated the coupled effects of heterogeneous investment strategies and heterogeneous risk tolerance on price fluctuations. In the market flooded with the investors with homogeneous investment strategies or homogeneous risk tolerance, large price fluctuations are easy to occur. In the market flooded with the investors with heterogeneous investment strategies or heterogeneous risk tolerance, the price fluctuations are suppressed. For a heterogeneous population, the coexistence of investors with pair pattern strategies and reference point strategies causes the price to have a slow fluctuation around a typical equilibrium point and both a large price fluctuation and a no-trading state are avoided, in which the pair pattern strategies push the system far away from the equilibrium while the reference point strategies pull the system back to the equilibrium. A theoretical analysis indicates that the evolutionary dynamics in the present model is governed by the competition between different strategies. The strategy that causes large price fluctuations loses more while the strategy that pulls the system back to the equilibrium gains more. Overfrequent trading does harm to ones pursuit for more wealth.
We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of log--normal and power--law behaviours. We then focus on the Bouchaud--Mezard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self--organises towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log--normal or the power--law form. This means that the first--order topological properties alone (such as the scale--free property) are not enough to explain the emergence of the empirically observed emph{mixed} form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with variable density of links. We show new results detailing how this effect is related to the higher--order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other.
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