Many agent-based models of financial markets have been able to reproduce certain stylized facts that are observed in actual empirical time series data by using "zero-intelligence" agents whose behaviour is largely random in order to ascertain whether certain phenomena arise from market microstructure as opposed to strategic behaviour. Although these models have been highly successful, it is not surprising that they are unable to explain every stylized fact, and indeed it seems plausible that although some phenomena arise purely from market microstructure, other phenomena arise from the behaviour of the participating agents, as suggested by more complex agent-based models which use agents endowed with various forms of strategic behaviour. Given that both zero-intelligence and strategic models are each able to explain various phenomena, an interesting question is whether there are hybrid, "zero-intelligence plus" models containing a minimal amount of strategic behaviour that are simultaneously able to explain all of the stylized facts. We conjecture that as we gradually increase the level of strategic behaviour in a zero-intelligence model of a financial market we will obtain an increasingly good fit with the stylized facts of empirical financial time-series data. We test this hypothesis by systematically evaluating several different experimental treatments in which we incrementally add minimalist levels of strategic behaviour to our model, and test the resulting time series of price returns for the following statistical features: fat tails, volatility clustering, persistence and non-Gaussianity. Surprisingly, the resulting "zero-intelligence plus" models do not introduce more realism to the time series, thus supporting other research which conjectures that some phenomena in the financial markets are indeed the result of more sophisticated learning, interaction and adaptation.
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