Co-Evolution Causes Instability: Differential Evolution of ZIP Automated Traders in a Simulated Financial Market

This paper reports results and analysis from simulation experiments in which a population of adaptive automated traders compete with one another and co-evolve their trading behaviors on a high-fidelity model of a contemporary electronic financial exchange. The automated traders are all using the adaptive Zero Intelligence Plus (ZIP) trading strategy, which was proven in 2001 to consistently outperform human traders in controlled laboratory experiments. ZIP adapts its trading strategies second-by second using a simple form of machine learning (ML), and for any one ZIP trader the performance of its ML is controlled by the values of five real-valued hyperparameters. The novel contribution of this paper is that here each ZIP trader has been extended to continuously use Differential Evolution (DE) to try to find the vector of five hyperparameter values that gives rise to the most profitable trading behavior in the current market conditions: this extended version of ZIP is referred to as ZIPDE. Because the current profitability of any one trader is largely dependent on the current trading behaviors of other traders in the market, and each trader's behavior can potentially be undergoing continuous change as a result of the simultaneous operation of the ML and DE adaptivity, this is an inherently co-evolutionary system. Results presented here come from long-term simulations in which continuous second-by-second trading interactions occur in the market continuously (24 x 7) for 365 days, during which some traders in the market will plausibly execute more than two million transactions. The results reveal that the continuous co-evolutionary interactions among traders give rise to unpredictable long-term instabilities in the traders' individual strategies. The instabilities seen in the new results presented here are qualitatively the same as those seen previously in simpler models of co-evolutionary markets involving less sophisticated adaptation mechanisms (i.e., stochastic hill climbers, rather than DE) operating on less sophisticated trader-agents (i.e., with PRZI agents rather than ZIP): thus, the results presented here add weight to the hypothesis that co-evolutionary markets are inherently unstable in strategy space, and hence that the long-term strategy instabilities seen in simpler simulation models of co-evolutionary markets are not mere artefacts of those models' simplifying assumptions. The Python source-code used in these experiments is being made freely available on GitHub, for other researchers to replicate and extend the results presented here.