Recurrence-Plot Visualization and Quantitative Analysis of Long-Term Co-Evolutionary Dynamics in a Simulated Financial Market with ZIP Traders

This paper reports first results and analysis from an accurate agent-based model of a contemporary financial exchange, populated by automated trading systems that are known to outperform human traders and that interact with each other via the exchange's {\em Limit Order Book} and in which the automated trader-agents are using a combination of real-time machine learning and optimization methods in an attempt to continuously improve their trading strategy, each forever trying to maximise their individual profitability. Because the profitability of any one automated trader's strategy is at least partially dependent on the distribution of strategies being played by all the other traders in the market, the system studied here is inherently {\em co-evolutionary}. Recent prior publications have explored the co-evolutionary dynamics of such markets populated with minimally adaptive ``Zero-Intelligence'' (ZI) trader-agents, a style of modelling with a long track-record in computational economics. This paper's novel contribution is that it presents the first ever exploration of the long-term co-evolutionary dynamics of such markets populated by co-evolving traders each running the {\em Zero-Intelligence-Plus} (ZIP) trading strategy, which was one of the first two trading algorithms demonstrated to consistently outperform human traders. Visualizations, via {\em Recurrence Plots} (RPs), are shown of the co-evolutionary dynamics of the ZIP-trader markets over hundreds of days of continuous second-by-second trading, which demonstrate that even when populated by super-human trading strategies, co-evolutionary markets can trace trajectories through strategy space that loop back on themselves, such that after many days or weeks or months of daily improvement to the strategy, it ends up back where it started. Recurrence Quantitative Analysis (RQA) methods are then used on the RPs to quantify the frequency of occurrence of such strategy-loops. Source code used in the experiments reported here is freely-available under the MIT Open Source License, on GitHub.