Timing under individual evolutionary learning in a continuous double auction

The moment of order submission plays an important role for the trading outcome in a Continuous Double Auction; submitting an offer at the beginning of the trading period may yield a lower profit, as the trade is likely to be settled at the own offered price, whereas late offers result in a lower probability of trading. This timing problem makes the order submission strategy more difficult. We extend the behavioral model of Individual Evolutionary Learning to incorporate the timing problem and study the limiting distribution of submission moments and the resulting offer function that maps submission moments to offers. We find that traders submit different offers at different submission moments the distribution of which uni-modal with a peak moving from late to early as the market size increases. This behavior exacerbates efficiency loss from learning. If traders evaluate profitability of their strategies over longer history, orders are submitted later with the same effect of market size.