Rank-size Distributions of Chinese Cities: Macro and Micro Patterns

A large number of studies have been conducted to find a better fit for city rank-size distributions in different countries. Many theoretical curves have been proposed, but no consensus has been reached. This study argues for the importance of examining city rank-size distribution across different city size scales. In addition to focusing on macro patterns, this study examines the micro patterns of city rank-size distributions in China. A moving window method is developed to detect rank-size distributions of cities in different sizes incrementally. The results show that micro patterns of the actual city rank-size distributions in China are much more complex than those suggested by the three theoretical distributions examined(Pareto, quadratic, and q-exponential distributions). City size distributions present persistent discontinuities. Large cities are more evenly distributed than small cities and than that predicted by Zipf′s law. In addition, the trend is becoming more pronounced over time. Medium-sized cities became evenly distributed first and then unevenly distributed thereafter. The rank-size distributions of small cities are relatively consistent. While the three theoretical distributions examined in this study all have the ability to detect the overall dynamics of city rank-size distributions, the actual macro distribution may be composed of a combination of the three theoretical distributions.

Heterogeneous Round-Trip Trading and the Emergence of Volatility Clustering in Speculation Game

This study is a detailed analysis of Speculation Game,a simple agent-based model of financial markets,in which the round-trip trading and the dynamic wealth evolution with variable trading volumes are implemented.Instead of herding behavior,the authors find that the heterogeneous holding periods in round-trip trades can contribute to the emergence of volatility clustering.In particular,the spontaneous redistribution of market wealth through repetitions of round-trip trades with non-uniform horizons can widen the wealth disparity and establish the Pareto distribution of the capital size.As a result,the intermittent placements of relatively big orders from endogenously emerged rich traders can bring on large fluctuations in price return.Empirical data are used to support the scenario derived from the model.

Role of Selective Interaction in Wealth Distribution

In our simplified description‘wealth’is money(m).A kinetic theory of a gas like model of money is investigated where two agents interact(trade)selectively and exchange some amount of money between them so that sum of their money is unchanged and thus total money of all the agents remains conserved.The probability distributions of individual money(P(m)vs.m)is seen to be influenced by certain ways of selective interactions.The distributions shift away from Boltzmann-Gibbs like the exponential distribution,and in some cases distributions emerge with power law tails known as Pareto’s law(P(m)/m−(1+®)).The power law is also observed in some other closely related conserved and discrete models.A discussion is provided with numerical support to obtain insight into the emergence of power laws in such models.