混合模型市场中幂律的出现
Emergence of Power Law in a Market with Mixed Models
摘要：
我们从资产交换的角度研究财富分配问题。帕累托定律在不同经济体、意识形态和国家中的强大性质表明，这可能是交易策略的结果。然而，简单的资产交换模型无法再现这一特征。一个码销售（YS）模型，其中投注金额是两个玩家的最小值的一小部分，导致财富凝结在一些代理人手中，而盗窃和欺诈（TF）模型，其中要交换的金额是输家财富的一小部分，导致财富的指数分布。我们表明，如果我们允许几个代理遵循不同的模型比别人，{ \it即}。由于存在着一部分主体服从TF模型，而另一部分主体服从YS模型的现象，导致了分布呈现幂律尾部。当一个人使用TF模型进行一部分财富的交易，而其余的使用YS模型时，也会观察到类似的效果。我们还观察到一个幂律尾财富分配，如果我们允许代理遵循的模式与一定的概率。
英文摘要：
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A yardsale(YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud(TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, {\it i.e.} there are some agents following TF model while rest follow YS model, it leads to distribution with power law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power law tail in wealth distribution if we allow the agents to follow either of the models with some probability.
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