Information Cost, Memory Length and Market Instability

In this article, we study the instability of a stock market with a modified version of Diks and Dindo's (2008) model where the market is characterized by nonlinear interactions between informed traders and uninformed traders. In the interaction of heterogeneous agents, we replace the replicator dynamics for the fractions by logistic strategy switching. This modification makes the model more suitable for describing realistic price dynamics, as well as more robust with respect to parameter changes. One goal of our paper is to use this model to explore if the arrival of new information (news) and investor behavior have an effect on market instability. A second, related, goal is to study the way markets absorb new information, especially when the market is unstable and the price is far from being fully informative. We find that the dynamics become locally unstable and prices may deviate far from the fundamental price, routing to chaos through bifurcation, with increasing information costs or decreasing memory length of the uninformed traders.