Technical Note: Parameterised-Response Zero-Intelligence (PRZI) Traders

Abstract

This brief technical note introduces PRZI (Parameterised-Response Zero Intelligence), a new form of zero-intelligence trader intended for use in simulation studies of auction markets. Like Gode & Sunder's classic Zero-Intelligence Constrained (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] that determines the strategy for that trader. When s is zero, a PRZI trader behaves identically to the ZIC strategy, with a flat/rectangular PMF; but when s is close to plus or minus one the PRZI trader's PMF becomes asymptotically maximally skewed to one extreme or the other of the price-range, thereby enabling the PRZI trader to act in the same way as the Shaver strategy (SHVR) or the Giveaway strategy (GVWY), both of which have recently been demonstrated to be surprisingly dominant over more sophisticated, and supposedly more profitable, trader-strategies that incorporate adaptive mechanisms and machine learning. Depending on the value of s, a PRZI trader will behave either as a ZIC, or as a SHVR, or as a GVWY, or as some hybrid strategy part-way between two of these three previously-reported strategies. The novel smoothly-varying strategy in PRZI has value in giving trader-agents plausibly useful market impact responses to imbalances in an auction-market's limit-order-book, and also allows for the study of co-adaptive dynamics in continuous strategy-spaces rather than the discrete spaces that have traditionally been studied in the literature.