تنظیم سیستم های اقتصادی در یک مدل چند ویژگی خودسازمان یافته انتقادی

We study the effect of size-based regulation on an economic system. A multiple-trait model of self-organized criticality is used to simulate the economic system. The major difference of this work from previous studies is that firm's fitness is not characterized by a single number but by M traits. Each trait represents one aspect of the competitiveness of the firm, and firm's size is one of these traits. Major finding drawn from the present study is that the effectiveness of regulations decreases with increasing M, i.e., size-based regulations are less effective when the overall fitness of a firm is determined by more factors

The concept and models of self-organized criticality (SOC) have been used in economic studies for more than a decade [1], [2] and [3]. One stream of this type of research is the use of Bak–Sneppen (BS) evolution model [4] to study the effect of regulations on economic systems [5] and [6]. To put it in a plain and simple way, BS model utilizes a circular lattice consisting of N sites to represent a ecological system, and assigns a parameter called fitness to each of these N sites. Each site represents a species in the ecological system. Higher fitness means higher probability of survival, while lower fitness implies lower barrier for a species to mutate or to be substituted by a new species. The evolution of the eco-system is simulated as follows. At each time step of evolution, the system is updated by locating the site taken by the species of lowest fitness and replacing that fitness by a random number drawn from a uniform distribution (ranging from 0 to 1). As this update will change the landscape of the ecology, the two neighbors of the updated site will have to adapt to the change by updating themselves through either mutation or substitution by new species—the fitness of these two neighbor sites will be replaced by two new numbers drawn from the same uniform distribution. The system will evolve all by itself into a critical state, at the critical state event of any scale can occur. An economic system can evolve in a similar fashion. Cuniberti et al. [5] use the BS model to study the evolution of a market. Cuniberti et al. consider that a firm's competitiveness or the probability of surviving market competition can be characterized by its fitness, and furthermore the firm's fitness is completely determined by the size of the firm. Cuniberti et al. introduce government regulations into the BS evolution model by changing the original Bak–Sneppen updating rule. By arguing that (some) regulations are in favor of small business, the new updating rule requires second update if a site sees its fitness jumps from below to above a threshold (the threshold represents a cutoff of regulation: the regulation is applied only when a firm is of a fitness higher than the threshold). The reason for the second (consecutive) update is explained as that when a small business becomes big business the government regulations will make it harder for the firm to adjust. In the model firms are divided into two sectors: firms smaller than the regulation threshold are in the lower sector (firms in this sector are referred to as small business), and firms larger than the threshold are in the upper sector (firms in this sector are referred to as big business). In Cuniberti et al.'s work a firm's fitness and size are treated as same without any distinction, therefore a firm's fitness is assumed to be determined solely by its size. In our view, this approach deserves further scrutiny because it is inconsistent with some well-established economics theories, for example, Porter's five force model [7]. In the five force model, a firm's size plays only part of the role to determine the fierceness of the market competition, other factors such as firm's products, asset specificity, and changing conditions of supply and demand also play important role to determine a firm's competitiveness or survivability, or in SOC terminology, fitness. In this work we will assume that a firm's size determines only 1/M of the total fitness, where M is an integer, i.e., a firm's fitness is determined by M equally-weighted factors and firm's size is only one of these factors. If some factors have more weight, they can always be divided into (smaller) sub-factors so that all (final) factors will have equal weights. As it is difficult to quantify exactly how big M should be, the objective of the present study is restricted to examine the effect of size-based regulations when firm size only contributes 1/M to the total fitness.

It is difficult to quantify exactly how much a firm's size will contribute to its overall fitness. For different types of business (e.g., high tech, banking, and retail) the percentage of firm size contribution to the overall fitness may be different. The objective of this work is to demonstrate that when a firm's fitness is determined by a number of factors (i.e., not by just a single factor) size-based regulations will have less effect than what it would be when a firm's fitness is assumed to be solely determined by its size. Assuming a firm's fitness was solely determined by its size, Cuniberti et al. studied the effect of regulations. One of their major findings is that if a firm experiences a very rapid growth a bad consequence may follow: the growth (a positive change) may lead the firm into trouble (bankrupt or major structural overhaul). Under the assumption that a firm's fitness is determined by M equally weighted factors, size-based regulations will make the critical level of fitness decrease monotonically with increasing M. To some extent this finding supports Cuniberti et al.'s results (M=1) by showing that size-based regulations will make some of large firms become small firms, but the regulations are less effective than what it would be for the M =1 case. Our study show that size-based regulations have substantial effect on size distribution of firms, and the net effect is to shift some firms from big business category to small business category (exact shape of the distribution depends on the nature of the implemented updating rule). In the mean time, non-regulated traits also show some responses to the regulations by lowering their minimums and averages. We emphasize that our result is merely based on an SOC model and government regulations are oversimplified. However, it still has the potential to shed some light on the likely effect of size-based regulations. Our model result suggests that size-based regulations will have the effect to reduce number of large firms and in the mean time to increase number of small firms with sizes just above the critical fitness. If this is true in the real world, the regulation will have a net effect to eliminate large firms and increase competition among small firms. The implications of these effects are complex: for example, fewer number of large firms favor monopoly, but the monopolists will not be long-lasting: they will be eventually brought down by government regulations (this is especially true if tax rate increases rapidly with firm size). As the multiple-trait model is analytically solvable [8], one possible extension of this paper is to divide the total number of traits into two subgroups: M1 traits that are size-related, and M2 traits that are not size-related (M1+M2=MM1+M2=M). If both M1 and M2 are let to approach infinity while keeping the ratio M1/M2 a finite number, the impact of size-based regulations could be quantified analytically.1 This potential extension is reserved for future study.