LGEM:یک شبکه مدل اقتصادی بولتزمن برای توزیع درآمد و مقررات مالیاتی

In this paper, a new econophysics model based on a lattice Boltzmann automata is presented. This model represents economic agents (people, countries...) as particles of a gas moving on a 2D lattice and interacting with each other. Economic transactions are modeled by particle-to-particle interactions in which money is conserved. If only particular transactions are considered (free market), the money distribution quickly converges to a Boltzmann–Gibbs distribution. But the model also introduces a third step of global income distribution that can be used for exploring tax regulation strategies. The model is presented, and some examples of income distribution are given. One of the most interesting features of the model is the fact that it is completely discrete, and it can be exactly implemented on any computational resource, leading to very fast, yet powerful simulations, especially when parallelization resources are available. Some results of these simulations, as well as performance data, are given.

Econophysics is an interdisciplinary research field which applies statistical physics methods for solving problems in economics and finance. The term “econophysics” was first introduced by the theoretical physicist Eugene Stanley at the conference Dynamics of Complex Systems held in Calcutta in 1995, as an analogy with similar terms such as “astrophysics” or “biophysics”, which describe applications of physics to different fields [1]. This novel discipline uses mathematical methods developed in statistical physics to study statistical properties of complex economic systems consisting of a large number of humans, and it can be considered as a branch of applied theory of probabilities [2]. In this sense, econophysics has much common ground with agent-based modeling and simulation, as it studies mathematical models of a large number of interacting economic agents [3]. Econophysics distances from the classical approach of economics, mainly representative-agent based, which ignores statistical and heterogeneous aspects of the economy. The main trend in econophysics can be reduced to a process consisting of 4 steps: (1) propose a micro-model that captures the essence of the economic interaction between two agents, (2) identify conserved quantities in the model, (3) integrate the micro-model to the macroscopic scale when millions of agents participate in the economy, and (4) get results and compare it with real data. In this paper, we are going to follow a different approach, inspired by a new trend in statistical mechanics, not previously applied to the economy field: lattice gas automata.

The models presented previously will lead to a global behavior different from the exponential distribution. The main feature is a reduction on the number of agents with zero money. It turns out that these distributions adapt well to real market distributions. For example, in [15], the probability distribution of income for US families with two adults in 1996 is given. In the same paper, the probability distribution of income for all US families in 1996 is also given. Both distributions can be seen in Fig. 4. The similarity between this distribution and the distributions obtained by LGEM is remarkable. Full-size image (33 K) Fig. 4. Probability distribution of income in the US in 1996. (a) Families with two adults. (b) All families. Figure options Considering the distributions obtained by LGEM models, and real data from economic systems, it turns out that these models can be very useful from a practical point of view. They can be considered as “toy models” to experiment with tax formulas or income redistribution strategies, before implementing in real systems. The main feature of LGEM is its simplicity and the universality of the results obtained. Just by adjusting a few parameters, almost any distribution can be reproduced. Additionally, the process by which each agent performs its evolution is a parallel, local process, with the only requirement, in some particular redistribution strategies, of knowing a unique global value. Al these facts lead to a very easy implementation. LGEM can be expanded in several ways to study new phenomena. As it has been explained, the money redistribution process has been designed to take place just in cases when a richer agent meets a poorer (m=0) one. New strategies can be designed to consider the possibility of a “charity transaction” to take place linearly with the difference of money between the two agents. On the other hand, economic transactions have been considered to take place completely at random. More interesting models can be designed, which consider different probabilities for winning and losing, as a function of the money of each agent. Finally, there is the last expansion that we are working on, and we believe it to be the most interesting aspect of LGEM: spatiality. One of the best features of LG is the fact that topology has a direct influence on the performance. A very interesting study would consist of having two different economic systems capable of interacting with each other in some particular sites. We strongly believe that the study of the interactions between systems can lead to a deeper understanding of global economy dynamics.