The demand–supply relationship plays an important role in an order-driven stock market. In this paper, we propose a stylized model by defining demand (supply) over a stock at a certain time as how many shares are on the bid (ask) side, which includes all buy (sell) limit orders and buy (sell) market orders. Also, we will treat the two types of shares as two different species with interaction (a single share corresponds to an individual of one species) and will construct and apply generalized Lotka–Volterra equations (Hofbauer and Sigmund in Evolutionary games and population dynamics, Cambridge University Press, Cambridge, 1998) to simulate how their population evolve based on some properties or assumptions of an order-driven market, and also on the heterogenous beliefs among traders. The model suggests that the population of bid and ask shares moves either to a fixed point or periodically without the impact of external information. Also, our model gives a reason, though it is not perfect, explaining why stock prices can behave chaotically.

中文翻译：

---

如果一个股票份额是生物个体：订单驱动市场中人口动态的程式化模拟

供求关系在以订单为导向的股票市场中起着重要作用。在本文中，我们提出了一种程式化模型，该模型通过定义特定时间内某股票的需求（供求），因为有多少股处于买入（卖出）侧，其中包括所有买入（卖出）限价单和买入（卖出）市场。命令。同样，我们会将两种类型的份额视为具有相互作用的两个不同物种（单个份额对应于一个物种的个体），并将构造并应用广义的Lotka-Volterra方程（Hofbauer和Sigmund在《进化博弈和种群动态》中，剑桥） University Press，Cambridge，1998）基于订单驱动市场的某些属性或假设，以及交易者之间的异质信念，来模拟其种群如何演化。该模型表明，要约和要约份额的总体移动到固定点或周期性地变化，而不受外部信息的影响。同样，我们的模型给出了一个原因，尽管它并不完美，但可以解释为什么股票价格会表现混乱。