No abstract

No abstract

Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue that 'fair play' for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α ∼ 3/2. In particular we relate it to the average number of individuals L depending on the average wealth: α ∼ L/(L − 1). Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β ∼ α ∼ 3/2. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ ∼ 2α ∼ 3. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for β and[Gopikrishnan et al. 1999] for γ).

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of namely between the resources available to the poorest and those available to the richest in a given society. The value of α is found to be insensitive to variations in the saturation term, that represent the expansion or contraction of the economy. The results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power-law distribution with 1 < α < 2.

We study the model of interacting agents proposed by Chatterjee (2003) that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation.We show that when all agents have the same fixed savings propensity, subject to certain well defined approximations defined in the text, these equations yield the conjecture proposed by Chatterjee (2003) for the form of the stationary agent wealth distribution.If the savings propensity for the equations is chosen according to some random distribution we show further that the wealth distribution for large values of wealth displays a Pareto like power law tail, ie P (w) ∼ w 1+a . However the value of a for the model is exactly 1. Exact numerical simulations for the model illustrate how, as the savings distribution function narrows to zero, the wealth distribution changes from a Pareto form to to an exponential function. Intermediate regions of wealth may be approximately described by a power law with a > 1. However the value never reaches values of ∼ 1.6 − 1.7 that characterise empirical wealth data. This conclusion is not changed if three body agent exchange processes are allowed. We conclude that other mechanisms are required if the model is to agree with empirical wealth data.