When one stock share is a biological individual: a stylized simulation of the population dynamics in an order-driven market

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.