Critical behaviour and system size in agent-based models: an explanation

The stylised facts of financial data, such as fat tails, volatility clustering, and long memory, have been successfully described within the paradigm of interacting agent hypothesis. However, a common problem that characterizes the dynamics of agent-based models is the necessary fine tuning of at least one of the parameters. In the class of models dealing with switching strategies based on continuous time approximation, it is, in fact, frequently reported in the literature a loss of interesting dynamics for an increasing number of agents. In this paper, we show analytically that this is equivalent to a modification of the time scale, that can lead to a “break down†of the desirable properties of the return time series. In order to show this, we have used a variant of the well-known model introduced by Kirman (1993), to treat stochastic transmission of information in an ants" colony. An increasing number of agents leads to invariant dynamical properties for a suitable choice of the time scale, while leads to a convergence to an uninteresting Gaussian regime for an improper transformation. We think that this occurrence is not limited to this simple setting, but it is applicable also to a more general class of models.