多主体市场中商品交换的动力学模型
Kinetic models for goods exchange in a multi-agent market
摘要：
我们介绍了一个系统的动力学方程描述的交换市场组成的两个人口的代理商（经销商和投机者）表示相同的偏好，两种商品，但在他们的交流应用不同的策略。我们通过价格理论中的一些基本规则来描述商品的交易，特别是通过使用交换的柯布-道格拉斯效用函数。投机者的策略是通过适当地影响商品交换的百分比，从交易中获得最大效用。这种微观描述导致了一个线性玻尔兹曼型方程系统的概率分布的商品在两个人口，其中后相互作用的变量取决于从预相互作用的商品在市场上的平均数量。在这种情况下，分析表明，投机者的策略可以将这两种商品的价格推向一个区域，在这个区域中，他们的群体有明显的效用。此外，一般系统的非线性动力学方程的玻尔兹曼型的概率分布的货物在两个人口的详细描述。数值实验表明，如何投机者的政策可以修改最终的商品价格在这个非线性设置。
英文摘要：
We introduce a system of kinetic equations describing an exchange market consisting of two populations of agents (dealers and speculators) expressing the same preferences for two goods, but applying different strategies in their exchanges. We describe the trading of the goods by means of some fundamental rules in price theory, in particular by using Cobb-Douglas utility functions for the exchange. The strategy of the speculators is to recover maximal utility from the trade by suitably acting on the percentage of goods which are exchanged. This microscopic description leads to a system of linear Boltzmann-type equations for the probability distributions of the goods on the two populations, in which the post-interaction variables depend from the pre-interaction ones in terms of the mean quantities of the goods present in the market. In this case, it is shown analytically that the strategy of the speculators can drive the price of the two goods towards a zone in which there is a marked utility for their group. Also, the general system of nonlinear kinetic equations of Boltzmann type for the probability distributions of the goods on the two populations is described in details. Numerical experiments then show how the policy of speculators can modify the final price of goods in this nonlinear setting.
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