Parameterised response zero intelligence traders

Abstract

Abstract I introduce parameterised response zero intelligence (PRZI), a new form of zero intelligence (ZI) trader intended for use in simulation studies of the dynamics of continuous double auction markets. Like Gode and Sunder’s classic ZIC trader, PRZI generates quote prices from a random distribution over some specified domain of discretely valued allowable quote prices. Unlike ZIC, which uses a uniform distribution to generate prices, the probability distribution in a PRZI trader is parameterised in such a way that its probability mass function (PMF) is determined by a real-valued control variable s in the range $$[-1.0, +1.0]$$ [ - 1.0 , + 1.0 ] that determines the strategy for that trader. When $$s=0$$ s = 0 , a PRZI trader behaves identically to the ZIC strategy, with a uniform PMF; but when $$s \approx \pm 1$$ s ≈ ± 1 the PRZI trader’s PMF becomes maximally skewed to one extreme or the other of the price range, thereby making it more or less “urgent” in the prices that it generates, biasing the quote price distribution towards or away from the trader’s limit price. To explore the co-evolutionary dynamics of populations of PRZI traders that dynamically adapt their strategies, I show initial results from long-term market experiments in which each trader uses a simple stochastic hill-climber algorithm to repeatedly evaluate alternative s -values and choose the most profitable at any given time. In these experiments the profitability of any particular s -value may be non-stationary because the profitability of one trader’s strategy at any one time can depend on the mix of strategies being played by the other traders at that time, which are each themselves continuously adapting. Results from these market experiments demonstrate that the population of traders’ strategies can exhibit rich dynamics, with periods of stability lasting over hundreds of thousands of trader interactions interspersed by occasional periods of change. Python source code for PRZI traders, and for the stochastic hill-climber, have been made publicly available on GitHub.