Zero intelligence in economics and finance

See the many examples in Tesfatsion and Judd (2006).

My thanks to an anonymous reviewer for this suggestion.

In this context allocative efficiency is the ratio of the actual gains from trade to the potential gains from trade.

\[--><$>\root\of{{\frac{{\mathop{\sum}\nolimits_i {({{a}_i}\,{\rm{ - }}\,} {{\pi }_i}{{)}^2} }}{n}} <$><!--\] where a_i is the actual profit achieved and π_i the theoretical equilibrium profit of trader i.

In order to be maximally efficient, it is necessary for trades to be conducted between intra-marginal traders (those who value the commodity at prices that allow them to trade at the equilibrium price). If extra-marginal traders are involved in trades then intra-marginal traders lose out and the total gain achieved is reduced.

In particular the constrained type of trader.

In contrast, markets such as the New York Stock Exchange simultaneously employ an order book and a specialist (the market maker) who makes strategic decisions in order to make profit while simultaneously supplying a service to traders such as liquidity and continuity of price.

There is an extensive literature on noise traders, including the highly influential papers by DeLong et al. (1989, 1990a, 1990b, 1991). In these papers noise traders are defined as behaving irrationally, though not necessarily randomly. The random behaviour of ZI traders could be viewed as noise-trader behaviour, but the class of non-rational behaviour is much larger than that of ZI behaviour, so not all noise traders are ZI.

The Hurst exponent characterizes the tendency of a time series to regress towards the mean. Low Hurst exponents, below 0.5, indicate a tendency to revert to the mean; high Hurst exponents, above 0.5, indicate that extreme events are more common. A Hurst exponent of 0.5 characterizes a random walk. See Mandelbrot (1997) for key work in this area in relation to finance.

Order aggressiveness was defined by Biais et al. (1995) based on the quantity of the order and the price relative to the best bid and offer quotes.

In many models, in particular those that are agent-based, the individuals do differ, for example, Gode and Sunder (1993a) in which each trader has their own supply or demand function. This does not cause a large problem in general for ZI models, as the simplicity of strategy aids in reducing complexity.